People want to fly into LHR. If BA moved out the void would soon be filled and they know it. This is just WW trying to protect BA's position as the main player at the airport.
As for building a new airport elsewhere and putting houses on the Heathrow site? Tens of thousands of people within a wide area around LHR work at either the airport or businesses that rely on the airport to survive. Closing Heathrow would have such a detrimental effect on that whole area. It isn't going to happen. Crossrail will go to Heathrow, the western rail access tunnel looks like it will go ahead. a second world class terminal has recently opened.
Heathrow isn't going anywhere. It needs better transport links and these are being upgraded eventually. It also needs the new runway and hopefully this will eventually go ahead.
Regarding the environmental concerns and air quality. We are talking about an opening date of around 2030 depending when someone actually makes a decision. The A380's and Dreamliners will be close to getting retired off by then. Aircraft, cars, trains, buses etc will all be far more economical. How can current air pollution levels be a factor when the timescales are so long?
Add to this the reduced stacking of aircraft awaiting landing slots and the fact that the plan, should it go ahead will allow the hub and spoke operation across the UK, using lower numbers of larger aircraft to operate the long haul services and be fed using efficient short haul aircraft from the regions.