Only two framebuilders near/in London are still truly functioning:

Witcomb Cycles (trained Richard Sachs amongst others) in Deptford. Barry is great to talk to.
http://www.witcombcycles.com/

Roberts Cycles in Croydon. See a lot of his frames down at Herne Hill being raced.
http://www.robertscycles.com/

Sadly, thats all we seem to have.

Ron Cooper still makes the odd frame but I think you have to be very patient, persistent and acquainted with him.

Don: Sadly Longstaff are in Newcastle and Lee Cooper are in Coventry so not that near london. For completness here are their websites:
Lee Cooper - http://www.leecoopercycles.com
Longstaff - http://www.longstaffcycles.co.uk/