Yay! Vintage in London....my fave topic!
A good place to start is Brick Lane in East End. There are quite a few vintage stores on Cheshire street which is off Brick Lane. The main one being Beyond Retro which is a massive warehouse full of cheap vintage clothes. You can get jeans for £5, dresses for £10.
There's another vintage cave on Sclater street which is really dingey looking but is full off vintage bargains.
Then there's Rokit on Brick Lane which sells vintage in an organised and accessible way. Very reasonable prices. There are branches in Camden Town and Covent Garden. The cheapest one is the one in Camden I find.
If you walk along Brick Lane, you'll find quite a few vintage stores all selling cheap-ish vintage stuff. On Sundays, you get Brick Lane market which is like a flea market and you can get SERIOUS bargains (I got a leather handbag for 50p once!)
On Hanbury Street, you have Absolute Vintage which sells the BIGGEST selection of vintage shoes you can imagine all colour organised. They also have a selection of vintage Burberry trenches all under £50. Oh and their cashmere selection is wicked too.
On Sundays, you get UpMarket near Dray Walk and Spitalfields market which has a few vintage stalls - all great for rummaging.
If you haven't spent your whole day around the Brick Lane area, then I would head over the Camden Stables Market where there are a ton of vintage clothing stores. It's a bit of a maze here, but it's great fun going around looking for stuff.