Not central London, but found this place a few weeks back www.houseofvapeslondon.co.uk Its on Shoreditch high street, so East London. Not the cheapest place I've been to but fantastic range. I visited the covent Garden vape shop and wasn't very impressed! House of vapes isn't that close to where I live but I'll definitely be going again soon!
Yes, we're quite poorly served in London. I buy everything online because I haven't been impressed with local shops - they tend to be very expensive and I've caught some of them giving very bad advice.
If you're worried about running out of juice it's worth scouting out local newsagents - more and more are carrying basic ranges of not-posh stuff.
There's a map here which will be useful for anybody in the UK trying to find their local shop.