GF, I was in the exact same situation as you a few years back, but lived a bit further up the road in N22. Anyhoo, here is my tuppence worth from the research I did all those years ago......
Stapleford: Only one school on site called, funnily enough, Stapleford Flight Centre. They offer training from PPL training to CPL/IR. Got a tie in the London Met Uni for the ATPL theory. Good school as they managed to get me through CPL/FI without too much fuss. However, a real ballache to get to without transport. The nearest train station will be Romford (depart Liverpool Street), over 7 miles away and the bus that runs from there to the airfield is not a very frequent service to say the least.
Elstree: Two schools, Firecrest Aviation and Cabair. Firecrest only do PPL level training, and Cabair do do commercial training, however, this is done at a different airfield to elstree. Does suffer from the neighbours and sometimes your circuits end up as mini cross countries. Getting to it is a little easier than Stapleford. Tube to Borehamwood (about 3 miles away) or train to Elstree (from Kings X) and about a 2 mile walk.
Having said that, if you travel outside peak time on the railway, you can take a bike on the train, which will take some of the hassle out of getting to and from the airfield.
Other places to consider.
Denham: Only one school there, conducting PPL level training. Much easier to get to on public transport as the train station is less than a mile from the aerodrome. Train runs from Marylebone or alternatively it's about 4 miles from Uxbridge tube.
Panshanger: Again, only one school. Watch yourself around the owner as he has quite a reputation. However, the instructors there are good so you will get the same quiality of training. Only trains up to PPL level. Train goes from Finsbury Park to Hertford North and a 2 mile trek to the field.
Wycombe: Two schools there. British Airways Flying Club and Wycombe Air Centre (just bought by Cabair I believe). Anyway, BAFC run up to PPL level and Wycombe Air Centre runs (did run!) a full commercial suite of training. Three miles from High Wycombe choo choo station and quite well served with buses.
Southend: Probably a bit too far out but still reachable in an hours train ride from Liverpool Street. Nearest train station is Rochford and it is on the airfield boundary so no long walks. Last time they were counted, there were three schools on site. Southend Flying Club, Willowair and Seawings. Cracking airfield with the best facilities of all with a full ILS, Lights and a lovely radar unit on site. Anyway, Southend Flying Club runs the full commercial package and are a fairly successful school. Seawings and Willowair run PPL level training only.
Good luck in whichever you choose, however, if you are considering going Commercial, please get yourself a Class One medical (only done at Gatwick) before you commence any commercial training (including ATPL ground school).
Websites
Stapleford Flight Centre
Cabair
Firecrest Aviation
Denham, The Pilot Centre
Panshanger
British Airways Flying Club
Wycombe Air Centre
Southend Flying Club
Willowair
Seawings