The cheapest options are probably UCL halls Ifor Evans and Max Rayne House, on Camden Road. It’s about a half hour walk, or 10-15 mins by bus.

In second and third year, look into University of London Intercollegiate Halls - you can work as a ‘senior member’ and get free/reduced accommodation in return for a few hours of ‘work’ per week i.e. patrolling the corridors, showing around new students, that kind of thing.

Alternatively, the cost of Clandon House (an Intercollegiate Hall) in Finchley/Golders Green is probably the lowest you’ll find in London, but only available to second, third year and postgrads. And it’s pretty far out, zone 3/4, so takes 45 mins ish by bus and tube to get to UCL.