Peter Capaldi (The Doctor) and Nigel Betts (Mr. Frank Armitage) are the only actors to play the same characters in both Doctor Who (2005) and Class.
Aaron Neil, who plays Ram's father Varun, previously appeared in The Magician's Apprentice (2015) as Coal Hill teacher Mr. Dunlop. His name appears on the memorial wall, so presumably Dunlop became either missing or dead off-stage.
Though canceled after one season, Class has been resurrected as a series of licensed audio dramas by Big Finish Productions, who have been producing licensed audio dramas set in the Doctor Whoniverse since 1999.
The building used for exterior shots of Coal Hill Academy is Cardiff University's Hadyn Ellis Building on Maindy Road, Cardiff.