For Cosmology, and arguably HEP, the best place in the UK is DAMTP at Cambridge, but they are very stubborn about taking their students from Part III of the mathematical tripos. And at Oxford, if you're interested in Twistor theory then have a look at the mathematics department, otherwise the physics department.
Apart from Cambridge and Oxford, the Physics department at Imperial is very good for HEP, if not the best in the UK; the maths department at King's College, London is also good for HEP. And also have look at the Institute for Particle Physics Phenomenology and the Institute for Computational Cosmology at Durham university.
For mathematical general relativity, besides Cambridge, the maths departments of Southampton and Queen Mary, London are good.
Hope this helps