Lots of places offer degrees mixing economics, politics, IR, history etc. in various combinations. Econ and politics and PPE (if you want to do PPE with a particular eye toward banking Warwick offer it, also York and Durham do it which are top unis, though all will be AAA) loads of places offer them.
More unusual combinations are often available at some of the big redbrick unis (Leeds, Birmingham and Manchester are where I'd particularly think of. They also tend to punch well above their league table ranking in terms of job prospects and if you like big cities are obvious choices) so have a look through their online course lists, and grades would likely be AAB rather than AAA.
PR I think depends a lot on making contacts, then getting work experience, then maybe a job. Keep a sharp eye on careers schedules when you get to uni for any potential talks by PR companies because they won't necessarily publicise their visits like law firms or the Big 4 do.
Plenty of people in law have politics or economics related degrees (if you still want some politics involved you could look at firms like Bevan Brittan which have a strong public sector emphasis). Just try and go to a well respected uni and get a good degree with all the usual extra curricular/work experience stuff. They seem to particularly love Oxbridge but after that, possibly because virtually all top 20 unis have AAA law students and they do still make up 50% of trainees, they're less discriminatory than investment banks seem to be.
Banking I don't know much about (do you mean IB or retail banking?), once you've found some courses you like the look of post in the 'is this course good enough for IB' thread and you'll get a much more informed answer than I could give you.
Business is open to anyone with any decent degree if the schemes from supermarkets, P&G, Shell etc. that make up the Times top 100 are what you fancy. Consulting wise I think it varies, the Big 4 seem to target a lot of different unis whilst Mckinsey or Oliver Wyman are fussier about where they target.
If you're interested in an international aspect to your degree, and have a European language, UCL offer a really interesting looking course in combination with various Sciences Po/IEPs around France.