Applying from US to Math Master's/PhD

Hi everyone,

I'm a math student in a US college, and I'll be getting my bachelor's degree next year. I'm interested in pursuing my Master's/PhD study in the UK. At the moment I'm looking at two Master's programs: Cambridge Part III and Oxford MSc in Math and Foundation of Computer Science. I have some questions:

1) How competitive is it to get into these two programs? (I think that if I can't get into Cambridge or Oxford, I'd be better off staying in the US.)

2) If I can get into one of them, how is my chance of getting into a PhD program at either of them? What about at other schools like Imperial, Manchester, Edinburgh, etc.?

I'm willing to pay for the Master's. As for the PhD, it would be great if I could get some funding (since I know tuition is expensive for international students), but I would still consider paying for it myself.

I highly appreciate your help.

I'm in my fourth year of an MMATH degree at Warwick, which is equivalent to being on the MSc year. I'm not applying for PhD courses.

For undergraduate at least (not sure how much this changes as you go higher up) Cambridge is regarded as the best for maths in the UK then the next level down you have Warwick, Oxford and Imperial in no particular order. So if you're looking at Oxford then you should consider Warwick and Imperial as well.

From what I've heard from people who are applying for PhDs, it is very competitive and you'd often study somewhere other than you would do it somewhere other then where you did your masters. Because of this competition, people are looking at going in the opposite direction to you and are applying to US places as well.