Interestingly, it is a little known fact that Gatwick is already a two runway airport.
The problem is they are too close together to permit concurrent operations (the second runway is used as a taxiway).
LAX recently moved its runway 20 metres; when you fly out of LGW you can see there is plenty of land to the south of the existing main runway for this expansion to take place; with far less impact than at LHR.
I don’t buy the inaccessibility argument about a THames Estuary; Jubilee line would be just as good as Piccadilly is to LHR, a fast MagLev style underground train from the West of London and the City would parallel the Heathrow Express.
Close LHR and use the land for a mixed housing retail/office development and ease pressure on Central London.