I live about 50m from the North London line/East London line (ie London Overground) near Canonbury station. I find the noise of trains, including the VERY large freight trains which run at night, FAR less penetrating than aircraft noise. In summer with the windows open it is a 545am awakening every single day as the first flights for Heathrow pass anywhere near ....would I accept even more aircraft noise - NO! Would I be contributing to legal action to stop any Heathrow expansion or relaxation of the current noise limits? Hell yes!
Do you live near any major roads? We're lucky, in that the road outside our house had been downgraded to B-road status, but it's still loud, especially in the morning. The A1(M) is still audible too, and that's a quarter of a mile away behind some houses. We keep our front windows sealed and double-glazed, even in high summer. Whenever I've been to London, traffic noise is the one thing I can always hear, in shops, in houses, everywhere except deep underground and at all times except a short period from midnight to about 04:00 (although cars still pass even then).
A countryman's perspective on London, living with that must drive you mad.