There have been a few discussions on the forum about this over the years, so you might find something via the search function.
IIRC, general feelings were that Bijan on TBR are good, as are Pure and Applied on Bermondsey St, although P&A are likely to be more expensive. We have two or three things done by Bijan, and are very happy with them.
Isn't there still an art shop at the top end of BHS, opposite the HSBC?
A friend, Sam, has a framing studio in the Alaska Buildings. We've just had 2 painitings framed and were very pleased with the work, so I'm not just plugging a friend's business without having used it! look up se1pictureframes.co.uk