I'm sorry to say that Gen Z do have a rep in the workplace as needing much more handholding than previous generations. Do you seriously think it will make him look capable if he can't use the vast world wide web to find somewhere to live?
@TinyDancer78 It sounds like somewhere slightly east or slightly south would suit him. The Thameslink goes south from Farringdon to Elephant and Castle, Denmark Hill, and Peckham. E&C (IMHO) is a bit ropey. But Camberwell (Denmark Hill station) and Peckham are full of young people, have tonnes of decent restaurants and bars (he can take you to the Camberwell Arms for a Sunday roast when you visit!), gyms and sports facilities. He can hop on a night bus there if he's out late late or an Uber won't be too much.
East is a bit more "trendy", but he could look at Hackney, Bow, Whitechapel, Dalston, Clapton. Easy to get to from his office, full of young people, and again, lots of facilities. I wouldn't go as far as Stratford.
Spareroom.co.uk is basically where everyone starts. Sometimes people let their rooms on a short term basis while they're travelling or whatnot, so that might be a good option if you/him don't want to commit to a long term contract.
I SERIOUSLY advise against him living alone (and you'd struggle to get anything for your budget anyway). London can be a lonely place, so he'll want people around him.
You could enquire about private halls, but your son might find he doesn't have as much in common/feel left out with those people if they're all living the uni experience and he's working a 9-5.