Photfusion has a really good darkroom for FB and RC and as it's about 30 minutes from Aldgate at the most on the tube, it's really not that far away! There are two other places I have heard of but have never been there, but I am sure are worth checking out. One in Oval, the other in Homerton/Hackney. Links here;
Of course I'm assuming you want BW. If colour, there is also Rapid Eye in Shoreditch/ Old Street run by some very nice people.
They also have BW RC facilities. Lee, the guvnor, is a good chap who is now also doing lots of teaching in colour printing to London colleges.
Hope you find somewhere to print.