I don't know to be honest.
If you're not happy getting a PhD from Wolverhampton then don't take it. However, don't let academic snobbery get in the way of what might be a good project. Although having said that, I would be highly suspicious of any supervisor with a poor publication output.
The scientist in me is shouting that it is really rather unethical to accept a PhD from a poor lab and then decline it after a comitment has been made. It costs a small fortune to readvertise it and to interview...
Just to be nosy, how much of a stipend does it come with, and what aspect of cancer research is it in.