There are many schools on the outskirts of London that offer PPLs. However as you progress with your training the numbers that offer CPLs and IRs get fewer.
As has already been mentioned the only two that I can think of in North / East London are
Stapleford and
Cabair - both offering a "joined up" modular course.
Stapleford is convenient because it is cheaper and easily reachable - either by train to Romford then a bus, or the Central Line to Theydon Bois then a bus or cycle. The groundschool is done at London Met (Tower Bridge) so, if you are still living in Stoke Newington, that's just a short bus/bike ride away.
Cabair is good because it offers you the chance to go abroad for your PPL / groundschool / CPL if you wish. However, in the UK, the CPL / groundschool / IR is done at Cranfield which is about 1:30h - 1:45h drive up the M1 if you were wanting to commute. There is B&B accommodation available in the local town.
I trained at both establishments so, if you need any further advice, send me a PM.