A lot of London's rubble was used to build and repair airfield runways around the south east. I have a vague memory of some vast amount (a million tons, millions of tons??) being sent out by train. I'd guess there'd be a similar amount that wouldn't be as suitable and need dumping somewhere...
Better rubble than what they threw in Beaufort's Dyke - the narrow but deep trench mid way between Scotland and Northern Ireland. That's where much of the surplus munitions, including chemical were dumped at the end of WW1 and WW2. There's even nuclear waste barrels down there. It's long overdue a cleanup as they're disintegrating.
http://news.bbc.co.uk/2/hi/science/nature/4032629.stm