OK there were several anon's responding which might/might not have been a bit complicated for some.
You seem to have a few quite difficult career decisions to make. Msc/MA course or go for more experience? If course then which course?
You’re right to identify some of the core skills that consultancies might require in the future. You identify analytical skills or more specifically statistics (fair enough that fits well with certain requirements). You identify economics (right some employers do specifically demand that or related disciplines).
If you have decided the course route, or indeed if you are still unsure, then start researching possible courses to address your possible skills gaps: Warwick (they have a Centre for Research in Statistical Methodology (CRiSM) but you would obviously need to research course outlines further), LSE (look at their courses if interested, their MSc Statistics or MSc Econometrics and Mathematical Economics might be of interest to you). Also consider other universities - asking Nottingham or Warwick? might oversimplify your alternatives.
Ideally the course you might go for would balance brand reputation, relevant course content (and of course all the other variables that you should be considering) against your eligibility for courses. Sure there are other ways of making the choice and describing how to make it but I hope we have been of some help to you.
I wish you luck - it can be a very tough area to get into.