somebody gave me a link to the CAA website where they have a list of approved flight schools in the Uk and abroad
There are two lists.
This one lists schools which offer training for the PPL in the UK, known as "registered facilities". For schools outside the UK, and for further training including CPL and IR, and also including integrated courses which take you from where you are now right up to fATPL, your school needs to be "approved" (rather than registered), and a list of approved schools can be found
here.
I would suggest that you start your PPL at a school near home - there are plenty of schools around London, and you're sure to find one you like. Some of them are approved for advanced training, but I think it would be wrong to make the decision based purely on whether the school is approved or not - all you need right now is PPL training at a school you are comfortable with.
Where in London are you? Especially since you don't have a car, knowing where you are will help us suggest which airfields have good transports links from your area.
FFF
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