Generally the top UK universities for pure maths correspond to the top unis here for maths in general. In no particular order the top 4 are more or less indisputably Cambridge, Oxford, Warwick and Imperial. Bristol is probably the next best, then Edinburgh and UCL. I think everything else is a bit more distantly behind those, although Edinburgh skews a but more to applied maths than UCL is my impression.
Note depending on the area of pure maths you want to study one may be better than the others. Warwick and Oxford seem to offer a lot more algebraic geometry and related areas, while Cambridge and Imperial seem to have a bit more offerings for number theory (although Oxford does have Andrew Wiles...no idea if he teaches, or if he does if he teaches well, however!). Oxford or Bristol are probably the best for foundations/logic and set theory as they have parallel strengths on the philosophy side of those areas from what I understand, and both have joint courses in maths and philosophy too. Oxford and Imperial seem to have the most topology, while Imperial seems to have the most geometry options, although UCL has a couple options in that regard too (possibly more tied to their GR work though? Not sure). Of course I'm not a mathematician so I can't comment on the actual strength of their research in their areas, and bear in mind just because a particular module/paper is offered doesn't mean it will be well taught! Also be aware that most of the differences in offerings indicated above are for the much more specialised third and fourth year options. The first two years there may be some differences in the exact order or sometimes depth some topics go into, but they'll all cover broadly the same material (because there is a fair bit of maths any mathematician needs to know to work in any field of maths).
However each of the top 4 offer their own maths masters programmes which overlaps a lot with their undergrad 3rd/4th year options, and I gather it's not uncommon for grads of one of the four to do oostgrad work at the others. So even if you don't get to take a particular course in final year(s) at one, you could still just as well do a master's and/or PhD at another that specialised more in the area of interest - and as indicated all will cover the material any mathematician (both pure and applied) "should" know. So you can't really go wrong going to any of those top four, or Bristol or UCL either. You can probably cover most if not all of the same material at Edinburgh, Southampton, or KCL as well. I think QMUL is a bit weaker though. Not so familiar with Manchester or Nottingham as far as maths goes though.