Unfortunately, the same thing also happens around small airports, and there the NIMBYs-come-lately often prevail.
https://www.bjtonline.com/business-jet-news/runway-removal-t...
https://www.bjtonline.com/business-jet-news/runway-removal-t...
Further expansion was approved in 2018, when one of the local MPs — Boris Johnson, who had promised to "lie down in front of bulldozers" to prevent expansion — was conveniently on a trip abroad during the vote it Parliament.
(The areas of London overflown are a mix of wealthy, average and poor-ish, left-voting and right-voting, it's far too large an area to wave away as X group of people complaining.)
Made worse because well off areas tend to be in the hills, and so planes are lower over the ground.