
Aircraft are a noisy, polluting nuisance. However, they are at present the only viable means of intercontinental travel and of domestic travel in bigger or lower-density countries.
Further, IME, most European regional flights operating from Heathrow are in smaller, less noisy planes like 737s and A320s.
So the question then, if noise is the problem, is really about volumes of intercontinental travel.
Now, onto London. In the post-Imperial age, London owes its continued economic power and prosperity to its role as a hub of various kinds. It's not like the UK has any major domestic manufacturing industry, or an automated inflow of stuff from the colonies, so London secures its place in the world by being a place of connection -- financially and culturally -- for world business and anglophone culture in general.
In a very real sense then, London's airports are what enables it to maintain its status in the world, and its levels of prosperity. The life of the city which you who live there choose(!) to call home stems from it being a place where people from all around the world choose to do business, congregate and visit for personal of professional reasons.
So you are called to make a compromise, and the question for you guys is, what is London's status as a global hub worth? It's not just about ongoing flights -- it's just as easy to connect through, say, Frankfurt or CDG. It's about how easy it is to keep your city a global hub of money and culture.
You don't get to have both prosperity and peace & quiet.