Imperial and Cambridge are the cream of the crop.
BiomedEng is a bit limited in terms of choices. The only accredited one i found are Southampton (they teach it in conjunction with MechEng) and QMUL which has a low satisfaction rate.
There is also Strathclyde and Glasgow, but neither is accredited as an engineering course which does worry me a bit since it makes jobs harder to land.
For EEEng it is a lot easier. As mentioned before, the next 20 universities are of approximately the same quality. Most RGs will give you a near identical experience. Some non RGs to throw into the mix are Bath, Surrey, Strathclyde, Loughborough, Swansea, and maybe Brunel. Just check UniStats to give you an idea of where the teacing quality is good.