I had a ball park quote about 2 years ago and a basement conversion is about £2000/2500 per sqm. obviously is can go much higher if you dig a lot (get yourself a pool
, etc as someone said. But still, 2 years ago the cost of space in battersea was about £7000 per sqm so still worth digging!
you can save a lot of money if you dig under your garden as you dont need so much steel beams (a garden is lighter than a house obviously!). The law says you can dig under your garden for about 1/3 of its size (check the precise numbers). I have seen some fantastic works of basement with no natural lights but state of the art extraction, I have also project managed a few for some of my clients.
The thing is London and particularly Wandsworth is one of the few boroughs that charge a lot for skips, and everything that disrupt the pavements. So for instance if you were living outside of the M25 you could knock off 30-40% of your total quote.
PM if you need more info. PS: I am not selling myself, i dont work on those sort of projects but do know a lot about construction