Or you could find out where they send it out to and go there yourself. Few camera stores process film in-house. Few do camera repairs in house either.
I've had this problem myself, both with development and repairs, and after going where they had their film and repairs done I found out that the turnaround was only a couple of day. The cost was lower as well!
Of course, with the demise of film, film processing facilities are getting harder to find. However, in a city the size of London, it shouldn't be too difficult to find a place that can do film development in less than 4 weeks, be it color or B&W.
And yes, 4 weeks has to be a record! In Paris, I could get pro film development in 1 hour at normal price and in 20' if I was willing to pay double the normal rate.