Oxbridge/LSE/UCL etc Economics Masters Chances

Graduated a year ago from New Zealand's top economics department with first class honours (7.25/9, 7.0 is required for first). It's ranked 50-100 internationally; respectable but hardly eyebrow raising.

I've been working in commercial banking since the start of this year at a global institution (though I don't think I'll mention it as I'll be leaving a grad program that's meant to be 18 months, might look suspicious). I also have two internships; both were at local corporates.

Long story short, I really enjoyed my honours year and have decided I would like to do further study, eventually to end up working at the UN or an NGO doing something development related. As the title suggests, ideally I'd like this to be at a top UK school.

Their websites suggest I have the minimum requirements to apply, but could someone please be straight up about my chances? Haven't taken the GRE yet, but assuming I get a solid score. Also am confident I can get strong letters of recommendation.

Further info:
-First in course in honours development economics;
-Second in course in honours trade economics;
-TA in undergrad trade economics;
-Dissertation in development economics/econometrics;
-Very strong score in honours econometrics.