I find most of the arguments on this thread ridiculous.
As FGMC says, "These airports weren't suddenly built to the size and capacity they are at now, they grew over many many years from being old wartime or aircraft manufacturing airfields.
If you could start all over again that would be great and your end result would't look like it does now, but you can't"
The best thing to do IMHO would be to accept that South East England already has enough airports, whatever their problems and limitations, and concentrate simply on first building a proper rail network, integrated into the normal rail ticketing at standard prices, to link all four London airports together. Then runways and development can take place at each of them and passengers can transfer between them for connecting flights or catch trains to a final UK destination. A properly designed rail ring will connect to all main lines east west north and south, benefiting everyone with a journey to make even if not by air.
Heathrow needs to be linked to Clapham Junction and to Gatwick so that long haul passengers can reach it from south and east of London. Also build a spur to Feltham and acquire the Heathrow Express extension from BAA and integrate into the national rail ticketing scheme. Right now connections north, south and south east of Heathrow are pitiful. A properly financed rail network (not one built on the cheap ... the British way) linking all airports to and also preferably through London would provide the infrastructure that the country needs. Yes it's expensive but look at the cost of not doing this.
This idea of a new airport somewhere east of London is just absurd. Build a proper ring of rail connections and it no longer matters where the airports are. Certainly no need to build more.