For colour print I've actually found the bigger Asda stores which have a film processor unit to be very reliable. Also they are very reasonably priced, particularly if you use the 2 day service rather than the 1 hour. If you have one near you, it's worth trying. Whether they do B & W C41 I don't know.
It's difficult finding reliable labs for conventional B & W films. Both Peak Imaging in Sheffield and the Fujifilm lab in Leamington Spa do black & white. I've never used them for this but they are reliable labs. You can also buy mailers from 7dayshop & others for Ilford's mail order B & W processing service. It's not particularly cheap and I've not been overwhelmed by the quality.