The elephant in the room is that everyone is asking the wrong question.
Should Britain's principal airport be located in the southeast corner ?
Surely our principal airport should be located closer to the centre, with good motorway and high speed rail links. A large swathe of open country will be needed together with a planning restriction to keep all new housing at least 5 miles away.
BHX would be a stong candidate for a new airport with 4 runways, an M42/M6 spur and a station on the new planned high speed rail link. The best future for LHR is closure for redevelopment on the very valuable land. Boris Island is a stupid idea, it is in the wrong place for everybody, even londoners.
This leaves London with 4 regional airports on the periphery which should be more than enough. None of these are candidates for a NATIONAL airport, they all take far to long to reach from anywhere other than London. For example it takes longer to drive from Bristol to LGW than to drive to MAN. For most of the country the southeast corner is a nightmare.