With one noisy take-off & landing every couple of minutes there's no need or opportunity to fly circuits to make lots of noise.
Are you suggesting that Heathrow & Gatwick are quieter places to live than Brize? Brize Norton is for the most part a sleepy hollow with relatively few ac movements per day, certainly compared to the 'glory days' of 3 ac in the circuit & a couple in the instrument pattern that used to be the norm at Lyneham. Even then the locals didn't use to complain much.
Personally though I did find the noise of a 15 ship formation starting up to be quite wearing. If I wasn't in it of course......