Stapleford and Damyns hall probably your best bet for rental or groups. You may also want to have a look at North Weald - it may not be that much further (time wise) than Stapleford for you and there may be a better selection of aircraft there. (Shame the old Central line isn't running anymore...)
And you might want to look at taking the train from Stratford to Southend airport (44 minutes, quite regular service) - there is some GA there and public transport could avoid getting stuck in traffic. Not sure where you've come down from, but driving in London it is very difficult predict your journey times - the first 20-30 minutes of any trip (i.e. getting out of the place) can easily become an hour or more, even on days where you would not expect it.
Good luck - enjoy.
B.