I presume your request was for powered flight, and I may be stating the b
ing obvious, but as you haven't had any lessons yet, have you tried the
UCLU Gliding Club? Could be a good starting point to get in the air, and you may meet like-minded individuals who you can get together with and even form a UCL Flying club to negotiate good rates with a local flying school.
Failing that I do know there's big rivallry between the London unis - I was at Imperial back in the day - but maybe under the shared kinship of London Uni's, you might be able to sneak into a flying society of a neighbouring uni? I thought Imperial used to have a flying society, and although I can't find any mention now you may be able to. Even if they won't let you join, you could talk to them and find out what flying school they use and convince the instructors there to match the rate for your lessons?
I'm sure if you "think outside the box" (
) like this you can find a way to get yourself a reasonable deal.
Just my two penneth ...
Good luck!