Msc/phd in pure mathematics

I need some advice,

I've just finished my 2nd year at UCL studying the Bsc in mathematics. I've so far really enjoyed my course and I'm hoping to go on to do a phd somewhere. Now, like everyone else, I want to go to the best place possible.

So far, my grades are fairly good, every exam I've sat I've gotten 90%+, except one applied module where I got 88%. I've spoken to certain professors at UCL and they seem very happy to take me on as a phd student after my third year, but I'm not sure if I should go to somewhere "better" or more prestigious.

I've done some research and I've decided that I want to stay in the UK for at least my masters (if I have to do one), but I don't mind going to the US for a phd. I've taken a look at Cambridge Part III and I've heard very good things about it, but there is a problem and that's the funding. Currently I only have £10k saved up, which would make Cambridge a very big stretch, while if I stayed at UCL I wouldn't have to do a masters, and I'd probably get funding also. I've also taken a look at Imperial's masters, and that's around £6k, meaning I could easily afford it and I could stay with my parents while studying for it. However, is Imperial really that much "better" than UCL? I understand how Cambridge can be seen as that, but I'm not so sure about Imperial.

Overall, I'm not sure what to do. Should I just stick with UCL or perhaps do another year at UCL and get a Msci then apply to other universities? Should I go to Imperial or somehow get more money for Cambridge... I'm not sure.

I'm not sure if there are many math experts in this forum, but I hope someone does respond.

note: my research area would most probably be something to do with Lie algebras and algebraic groups.

Here is a link to what we study at UCL: http://www.ucl.ac.uk/maths/courses/undergraduates
Imperial masters: http://www3.imperial.ac.uk/pgprospectus/facultiesanddepartments/mathematics/postgraduatecourses/puremathematics

Hope someone can help, thanks.

edit: I hope to go onto academia, failing that, finance - so prestige is important.

It's unusual for something to score such a high 1st to do a masters.

I suggest you go straight to a PhD and head to the US, where you could get some generous bursary / scholarships.

Thanks for your response,

I'll most certainly look into it but I don't think I'm that competitive. I only have one summer of research and nothing published. I'll try to do something next year, but we'll see. Also, for practice I usually do worksheets/past papers from other universities. Some European universities have insanely hard worksheets, harder than most of the Cambridge ones and most certainly UCL's. So when doing these, I usually always need to look up how to do the problem, or spend a few hours on it. Students from these universities would most certainly be more prepared than me for a mathematics phd - so I really don't think I'm competitive for any US scholarships.

Thanks for your response,

I'll most certainly look into it but I don't think I'm that competitive. I only have one summer of research and nothing published. I'll try to do something next year, but we'll see. Also, for practice I usually do worksheets/past papers from other universities. Some European universities have insanely hard worksheets, harder than most of the Cambridge ones and most certainly UCL's. So when doing these, I usually always need to look up how to do the problem, or spend a few hours on it. Students from these universities would most certainly be more prepared than me for a mathematics phd - so I really don't think I'm competitive for any US scholarships.