I started training for my PPL after my GCSE's and it took just under a year. This meant I ended up doing a lot of theory around the time of my AS's. I didn't find it massively difficult because I was interested in the flying subjects and so it didn't feel like lots of extra work. I did the flying on the weekends and it was roughly an hour a week, which spreads out quite comfortably. If you have the resources and determination then I say go for it.
Whereabout do you live in London? probably easier to recommend schools once it's clear which airfields you live close to.