Unfortunately you won't find many quilt shops in London, for all sorts of reasons - quilting isn't as popular here as it is with you guys, ergo there isn't the same market, the cost of having a shop in London is prohibitive etc, etc. Also, be prepared to spend around $23 for a metre (39") at current exchange rate. Although not a quilt shop, many branches of John Lewis (a department store) have a haberdashery department, stocking mainly Amy Butler fabric. I'd suggest you phone first.
Beyond Fabrics
Stitch Up
MacCulloch and Wallis
These are a few fabric/haberdashery shops I found from our business directory 'The Yellow Pages' and have websites for you to have a look at. Good luck!