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The Research Assessment Exercise (RAE) is one way of getting a feel for quality of research at institutions. It's not foolproof - universities can be quite strategic in what they submit so as to try to improve their score, but it does give yoau feel for who the big players are. The specific rankings you might be interested in are:
Cancer
http://www.rae.ac.uk/results/qualityProfile.aspx?id=2&type=uoa
Pre-clinical and Human Biological Sciences
http://www.rae.ac.uk/results/qualityProfile.aspx?id=15&type=uoa
Other Laboratory Based Clinical Subjects
http://www.rae.ac.uk/results/qualityProfile.aspx?id=5&type=uoa
Off the top of my head for the fields you mention I would look in London (UCL, Imperial College, Kings College, Institute of Cancer Research, QMUL), Cambridge, Newcastle, Bristol, Manchester, Oxford, Leeds, Birmingham Nottingham and Glasgow. They all seem to have decent RAE scores, plus are generally regarded as good universities (apologies to any I have missed out!) For biomedical research I personally think it's good to go to a uni that has a medical school whose staff are actively engaged in research, even if you ultimately end up working in a non-clinical group.
As well as the above, Cancer Research UK have a number of dedicated research facilities of their own, as well as funding research in universities: http://science.cancerresearchuk.org/research/centres/
Another suggestion would be to look at papers you're reading on work you find interesting and see where the research is coming from. Or look at the big conferences in those fields and see where the names relating to your areas of interest are from.
Good luck!