Re: The most amazing engineering
BA are not the ones asking for the third runway to be built. Heathrow Airport do. And quite frankly, Heathrow *does* need a third runway. However, I *do* believe that the number of flights should roughly remain the same for the airport (perhaps increase by 10% but with strict no-night-flights limits except in limited circumstances) even if the third runway were to be built, primarily because the third runway would allow the flexibility for existing flights to continue even in inclement conditions (like heavy fog, heavy winds, snow, etc), whereas right now, countless flights are cancelled and cause endless misery to those who have no option but to travel when they're scheduled to travel.
While I commiserate with the burghers of Eton, Windsor and Maidenhead, be aware that most modern airliners are a damn sight quieter on takeoff and landing than the oldies (like BA's venerable 747s and 767s with the old RB211s or some of the US/ME 777s with their GE90s!), and that what you have experienced is LHR trying to find a way to be less intrusive where jet noise is concerned by spreading the intensity across different paths. That it's catching you out now is... well... unfortunate.
I certainly would *never* believe a politician who tells me that "we will *never* allow this to happen" if it affects my future home.