Path to Finance(IB) for Strong Quantitative Student

I'm a top 0.5% student of engineering, and am very good at math and have strong quantitative skills. Very interested in finance, IB concretely, and quite knowledgeable, have very limited experience though, apart from studying finance courses at another university parallel with my current one.

All in all, I'm a great student, but have no finance internships, but I can do one at my country's Central bank, but thats not finance but macroeconomics, is it relevant? Should I do it? What do you suggest?

More importantly, should I try to get in some MFin program at LSE/Oxford or at some other European school, so as to get further exposure to IBanks and easier to get contacts, and do you think I have good chances of getting in? I expect a really high score on GMAT :)

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