LHR is accessable from four points of the compass, by road at least but lacks rail access from the west and south. Thames Estuary would only have access from three points of the compass. Most of these will require travel via London. Even if there is a MagLev style train from London it still requires people to travel to London.
LHR and LGW are the best placed airports with relatively easy access, LGW being better connected by rail than LHR. Not everyone lives in London. It is a non-starter really as the wildlife aspect will stop it.