It used to be JD: “I always had a sneaking suspicion that Johnny Depp wears it when he’s in town!” Dench says to the manager. “No,” she replies firmly. “You are the only JD who stays here.” But, anyhow, that’s all irrelevant because it’s been upgraded to “DJD”. “Heaven!” Dench growls with delight. “I love it.”

For such an impeccably mannered Dame, Dench has a very low, dirty laugh that builds up steam – “huh huh huh” – like a car ignition. Despite the fact that she is 80 this month – “Ahhhh, 49 at last!” she says when I bring up the birthday – Dench lives her life like a woman half her age.

Her filming schedule is busier than ever. She travels and she still gets good, stretching parts. (Philomena, Barbara in Notes on a Scandal, Iris Murdoch, Elizabeth I. She wants a “dangerous” one next.) We are about to see her over Christmas opposite Dustin Hoffman in a BBC film, Roald Dahl’s Esio Trot.

“Energy I have,” she says. In 2011, for example, at 77, she made four films back-to-back, including J Edgar, directed by Clint Eastwood, in America and The Best Exotic Marigold Hotel in India. Ten years before that, she famously threw herself into filming in the same way, but back then it was to try to cope with the grief of losing her husband, the actor Michael Williams, to lung cancer (then she made three back-to-back).

Now, her life is much happier. A lot of this is to do with the fact that, after more than a decade of widowhood, Dench is no longer single. “I am terrible on my own. I am really conscious of being in a room. Walking in is agony to me. Therefore I wouldn’t do it.”

“Boyfriend” doesn’t feel quite the right word to use for the love interest of an 80-year-old dame, but maybe she’d approve of it being straightforward. Dench’s new boyfriend is called David Mills, an ex-Jersey farmer who built a wildlife centre dedicated to British animals on his family land “just a few fields away” from Dench’s own acres on the Surrey/Sussex border.

Although Dench admits she has been attracted to “quite a lot of men over the years”, she says a new relationship after losing Williams “never even for a second occurred to me, not for a single second”.

She was famously blissfully married to Williams. They had met at the RSC and become good friends, sharing the same naughty sense of humour. Her best friend, Pinkie Kavanaugh, who died last year (“I miss her dreadfully”), had thrown her her wedding bouquet. And then, in 1971, at 36, Dench fell in love with Williams, married him and had their daughter, Finty, a year later.

She had 30 years with him. He gave her a red rose every Friday and advised her on all her parts. It is Williams we have to thank for Dench playing M in 13 Bond films (her last, much to her chagrin, being Skyfall).

“When the offer first came in for GoldenEye, he said, ‘Oh God, you must do it! I long to live with a Bond girl’,” she recalls. As well as their happy marriage, they worked together, on the stage and for television, most famously in A Fine Romance in the early Eighties.

A couple of years after Williams died, David Mills asked Dench, an instinctive lover of animals, if she would open the new badger enclosure. “And although I was filming, I just wasn’t in good enough shape to do something like that.”

But, she says, he “stalked” her − “Yes! I think he did.” Seven years later, in 2010, she agreed to open the red squirrel enclosure. The squirrels were the clincher. Did you resist him then too? “I don’t think I did,” she says. “Ooh, how shocking!” Her chest rocks up and down with her dirty laugh again.

The relationship – “I wasn’t even prepared to be ready for it” – started from there (Mills is divorced and a few years younger), helped along by their mutual love of wild cats, badgers, otters and pretty much anything with fur, teeth and claws. “It was very, very gradual and grown up. We got together, in a way, through the animals. It’s just wonderful.”

She recalls a birthday dinner four years ago in the “Cov Gar”, organised by Finty, with her close friends present. Was he being vetted? “I think everybody was vetting each other,” she says. Huh huh huh.

Dench somehow managed to keep the relationship out of the press for a few years. In a newspaper diary it was insinuated that Dench is now considering marriage again. This, however, seems very wide of the mark. She tells me they don’t live together and have no plans to start.

“We are much too independent. And he is very busy. He has a business to run. But he is soooo lovely, with a great sense of humour. Now it’s absolutely wonderful because there’s somebody who makes me laugh. Isn’t it lovely?”

In a new book of photographs from her life, Behind the Scenes, there are a few pictures of him that Dench has chosen to include; she is beside him, either laughing that dirty laugh or smiling. He has a mop of floppy silver hair and a kind smile. They clearly have a lot of fun.

Recently, she took him to Los Angeles – his first visit – where Dustin Hoffman was presenting her with a Britannia award (given by the LA branch of Bafta). “David was like this!” she says, miming the craning neck needed for celebrity spotting.

In the back of the car, on the way to the ceremony, he started yawning and told her: “I’m not yawning because I’m tired. Baboons yawn when they are frightened!” She loves this kind of thing. It makes her howl with laughter.

“Love” is not a word that has been spoken of, she says. “I’ve never said those words.” Perhaps she is cautious? She says she lives in the moment.

“I have ‘Carpe diem’ carved on a piece of stone by my front door. It sounds rather grand, but it’s a very good motto, because what’s the point of waste? You never know what is going to happen tomorrow.”

Mills was at the hotel with her last night, for the premiere of Esio Trot, but now he’s gone back to the wildlife. They are from different worlds, she says, but she loves his world of furry animals as much as he loves hers of sleek A-list stars. (Alongside her two older brothers, one still alive, the other recently deceased, Dench grew up in York with 17 stray cats and a dog.)

Roald Dahl’s Esio Trot is a film of a Roald Dahl book that tells the story of a shy old man who tries to win the heart of a woman who is obsessed with her tortoise. Dench plays Mrs Silver as a bosomy, red-headed, sexy northern widow who has secretly been wanting all along to get her hands on the shy, virginal Mr Hoppy (Hoffman). It’s a love story of old age blossoming among animals (60 real tortoises, 40 fakes on the film set).

Hoffman adored Dench and she, in turn, says she was “bewitched” by him. “Oh, he’s a beauty. A beauty, really self-deprecating, and the way he runs it down. I love it! I love! And he’s wonderfully naughty, gloriously naughty.”

During the press conference, they stroked and patted and held hands. Hoffman has called Dench a “scrumptious woman all her life”. Early pictures show a sensual, plump round face and pleasingly normal curves rarely seen on today’s young actresses.

Hoffman – who has a much younger second wife – told her that if he’d known her back then, he’d have never let her get away. Sitting on the sofa drinking her coffee, Dame Judi repeats the line to me wistfully. “He said, ‘I’d never have let you go!’”

Clever old David Mills then, for not letting her go; for waiting seven years and finally enticing her over the garden fence with his red squirrels. What does he make of it all? “He’s taken to it like an otter to water,” she says, chuckling.

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Dame Judi Dench’s grief for Michael Williams has changed over time but never left her. “It becomes different. It alters. It doesn’t become any less. Only the other day, I opened a drawer and then shut the drawer and there was Mikey’s photograph on the floor. I was able to go, ‘Ooh, how lovely!’ whereas before I would perhaps not have been able to cope.”

Williams lived long enough to see Dench’s career change – or rather develop – from the stage (she’s played all the Shakespearean great roles) to the big screen, sealed when she was nominated for an Oscar for playing Queen Victoria in Mrs Brown and then won one for Best Supporting Actress in Shakespeare in Love in 1998. (There have also been six Oliviers, six film Baftas, four television Baftas and a Tony.)

At her age, of course, she is losing her friends and family. This year, after Pinkie, she lost Jeffery, one of her elder brothers and “one of the longest serving members of the RSC”.

Dench cites Jeffery as the inspiration for her decision to ditch theatre design to attend the Central School of Speech and Drama, from which she went straight into the Old Vic Company, playing Ophelia. There is a photograph of them together, in old age, in which they look remarkably similar. She becomes very quiet. “Hmmmm. Hmmm,” she says, looking away.

She spent time with him in Cornwall in the summer of 2013 and had intended to take David to meet him, but he died sooner than she expected.

And of Pinkie, too, she says: “I miss her dreadfully. I always used to think, ‘I’ll ring Pink up and have a good moan’.”

Dench is much more famous than many of her early actor friends (Dame Maggie Smith aside, whom she calls “Mags”), but her late-found international fame was never remotely relevant or even felt. “It simply isn’t the case that the best actors are the ones in work. I remember seeing Pinkie in Sabrina Fair in Frinton. She was so good … God, she was good.” Her voice trails off.

“We went through everything together. Everything. Marriage, babies, her divorce, Mikey dying. I’m sure other people have that … But I’ve had and have such good friends. You’re lucky to even have one like that in a lifetime.”

Friendship and being part of a gang, family or film, is everything to her. For a long period during Dench’s marriage, they lived happily with Williams’s parents and her “ma” in Charlecote, near Stratford-upon-Avon. They are all buried there; Dench’s father, Reginald, who was a GP; her mother, Eleanora, who was a wardrobe mistress at York Theatre; Williams and his parents, too.

Later, when Finty had her own baby – “my Sammy”, Dench calls her 17-year-old grandson now, a dead ringer for Ed Sheeran – they lived together in her house on the Surrey/Sussex border, where she is today. In the garden, there is an armillary sphere, on which is engraved a quote that Williams would say to them: “When we are together, there is nothing we cannot achieve.”

It is only relatively recently, when Finty and Sammy moved to London, that Dench finally had to face living on her own. But this month Finty is coming for a bit while she is in a play, and Sammy – “Oh, I dote on him. It’s heaven” – visits most weekends. He calls her “Ma”. And there is a housekeeper who keeps the show on the road and a PA who helps her answer her letters.

Today, her make-up artist, Em, is waiting in her room and she’ll have a lobster and chips lunch with her. Later, they’ll have a glass of champagne together. (“Champagne is my only drink.”) On set with Hoffman, too, she regularly tried to get him to go out, but he always needed a nap. Richard Curtis, writer of Four Weddings and Notting Hill and now Esio Trot, says affectionately of Dench that she is “very badly behaved”.

Almost 70 years ago, on her first day at her Quaker boarding school in York (she is still a Quaker), she let off a fire extinguisher while “horsing around” with a chum. The girl is still her friend today: “We speak on the phone every Sunday.” Clearly, there is still a lot of “horsing around” going on. “I don’t want to work with anyone who can’t laugh at themselves or make mistakes or look foolish,” she says.

Billy Connolly, after acting opposite Dench in Mrs Brown (the film that really brought her to the attention of Harvey Weinstein, one of the producers of Shakespeare in Love), said of her: “You know those English twittering f***ing women – they think she’s one of them, and she isn’t.”

Once, for a Bond premiere, Dench had a 007 Swarovski crystal tattoo applied to the back of her neck, and another time, she got her make-up artist to put a fake tattoo saying “Harvey Weinstein” on her “arse” – a very Dame Judi word. When the rapper Lethal Bizzle coined the phrase “dench” for “cool”, and used it on his clothing range, she bought the cap and the T-shirt. Today, she wears a boho collection of necklaces and rattling bangles.

Dench loves the comedians she’s worked with, such as Connolly and Steve Coogan on Philomena. “How dare they be so good at this? I said to Steve, ‘Get back!’ Straight acting is not their bag. They should be [on the stage] making jokes and yet they come to a film and wipe the floor with the lot of us.”

During one play, she and Kenneth Branagh were sent home from rehearsals in disgrace because they couldn’t stop laughing.

That Dench makes a point of mentioning Mills’s humour as one of his attractions is unsurprising. She loves people who make her laugh. And she loves animals. Filming Esio was a joyous combination.

“But what about the orchid mantis?” she exclaims of Life Story, the BBC wildlife programme that can melt even the steeliest of hearts. “And the barnacle goose? Who wants to be a barnacle goose? You lay an egg, you go through all that …”

Dench starts straining as if she is trying to push out an egg of her own, her voice forced with the effort of laying: “Tr-y-i-n-g t-o la-y a-n e-g-g… and then the poor thing hatches and has to throw itself off a cliff and gets eaten by a wolf! Christ almighty, we’re lucky!” Huh huh huh.

A couple of strangers are sitting on a nearby sofa side by side bolt upright. What dynamite for them to see Dame Judi give an impromptu performance as a barnacle goose. “Do I know those people?” she whispers, peering over at them.

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In the third stage of Dench’s life, she is top of the tree. She has been professionally liberated, poignantly, by widowhood – “This kind of filming would have been very hard on Mikey, very hard indeed” – and yet now is no longer alone.

She is in the middle of filming Richard III with Benedict Cumberbatch, in which she plays the Duchess of York, and has finished the sequel to The Best Exotic Marigold Hotel, the story of a group of older people who decamp to India to stay in a hotel rather than a face the deathly prospect of a care home.

In Behind the Scenes, Dench includes a picture of herself in her garage, beside a very bling BMW, which, because of her eyesight, she can no longer drive: “I just lean against it. It makes me feel about 29. It’s not to do with age, it’s the engine. You’ve got to keep the engine going.”

Roald Dahl’s Esio Trot is on BBC One on New Year’s day at 6.30pm

Shoot credits
Make-up: Emma Page using Chanel Christmas 2014 and Sublimage L’Essence