There's Silverprint in Valentine's Place (just off Blackfriars Rd, near Webber St. junction). But, they are serious photographers' suppliers and I have been told that they are top of the game on that score, so probably won't be cheap but worth a call perhaps.
as snappy snaps london bridge is no longer, i went to the branch just over waterloo bridge on the strand.
here is a link snappy snaps
the result was ok and they scan it on to a cd if you like.
as they are franchises, the quality varies, but try one film and see maybe.
It is not SE1 but I have used RG Lewis in Southampton Row, just north of Holborn tube. A lot of professionals buy their kit there and they try to use good quality developers and printers. not sure about price these days.