There is one elephant in the room. You can increase capacity on the ground at LHR or STN or LGW, but has anyone noticed that the airspace above London is pretty much at maximum capacity. Have NATS been consulted about how they will handle the increase in traffic? It is normal these days to be handed over to a London frequency and not be able to get a word in edgeways until you have already transited that controller's area of authority.
There's a lovely big runway sitting at Manston that has all it's approaches from over water. Just build decent road/rail links. Kent will welcome the extra revenue.
How about moving most of the long haul holiday traffic to some of the regional airports that are currently withering on the vine. People happily drive hours to London airports for their annual holidays to the Caribbean or Far East. Why not redirect them away from the Capital?
But of course, no one in Westminster wants the annoyance of having to get on a motorway to start their holidays....