FlyingJones
Looking at EBOS' location geographically it looks like the closest would be Biggin Hill. However, Stapleford is an option as it has a tarmac runway as is Elstree.
I fly from Elstree and it is a short cab ride to Borehamwood Station. The café is also very nice. Stapleford has Chigwell Tube Station a cab ride away so you're sorted getting into London.
Whereabouts in London are you looking to go?
As suggested by Alex, Southend might be an option as it's much closer to you and it has a fast rail link into Liverpool Street. But it is an airport in the proper sense, and not a GA aerodrome like Elstree.
I guess it also depends on which type of airfield you'd like to fly into as well.
Good luck
