Neither will get you into MBB. Try Oxford or Cambridge instead.

Sadly, good advice. Harvard and Insead are the only realistic alternatives to LBS and Oxbridge if you want to get into MBB. MBS, indeed, has placed into McKinsey and even has a summer associate there right now, but it's much easier from the top schools.

I see. What about for non-MBB consulting firms -still LBS/Oxford/Cambridge/Manchester?

This depends on the firms you are looking at. Read: How to use LinkedIn to find the best school www.find-mba.com/board/33571

Looks like 43% of Imperial's class of 2013 went into consulting:

http://wwwf.imperial.ac.uk/business-school/programmes/imperial-mba/career-support/graduate-destination-data/

McKinsey is on the employer list.

So at Imperial BS there are almost more recruiters than students? :) I was interested myself in it and did some research:

Imperial's MBA program is placed at the 34th position in the FT ranking (http://rankings.ft.com/businessschoolrankings/global-mba-ranking-2015) while fees are pretty the same (55.000 euros) of other much better ranked schools. Also 43% of Imperial students going into consulting means 20 students.. the program is very small with an average of 52 students (http://www.topmba.com/where-to-study/europe/united-kingdom/top-business-schools-uk-201314), and a small alumni's body. Even if they claim that their admission process is highly competitive, it seems to be one of the less selective business schools around (http://poetsandquants.com/2015/01/03/the-most-least-selective-international-business-schools). Paying attention to marketing is the first skill you should acquire before choosing an MBA program.
If you aim at brands, then Oxbridge should be a better choice, but if you aim at consulting.. then Insead, and LBS, are by far the best choices. Get a look at the McKinsey targeted school list for a better insight on the best business schools for consulting: http://www.bloomberg.com/bw/articles/2012-11-05/mckinseys-go-to-business-schools

In any case, as the labour market is extremely competitive today, and the consulting field even more and depending on your profile much more than from the MBA you came from, in order to be prepared to land other jobs I would never go over the best 3 business schools in Europe according to the FT ranking (the ranking of the rankings): LBS, Insead, IE. And these three schools are McKinsey's european targeted schools of that list too! (consider that, as for HBS and NYS, LBS is not in the list because it didn't provide data, but from where McKinsey actively recruits from..)

Other top tier european choices are Iese, IMD, HEC, and Oxbridge (who offer good programs and very spendable brands..). These are the best european BS offering an MBA program, except IMD who has only the executive format, but having the best industrial management and leadership program in Europe certainly deserves a place in the top tier european BS list.
Also the GMAT best school's list supports these considerations pretty well: http://find-mba.com/board/gmat/gmat-tiers-strong-schools-for-your-gmat-23247

That's great advice from Global MBA. LBS/Insead are certainly the top feeders into the European/UK MBB consulting firms, with Oxford/Cambridge probably the next tier down.

The Linkedin data is a bit interesting, though. For the UK, these are the top listed schools for people in management consulting:

1. Open University
2. LBS
3. Cranfield
4. Warwick
5. Henley

Not sure what to make of that.

Combine data with common sense and other research. Analytics/data on its own provides little value.

OU is a huge school, but widely used for part-time study. Look at outcomes as a % of each school's whole alumni body.

Wow, thanks everybody for the input!! Looks like I'm going to hone in on LBS and Oxbridge + Manchester. I've got to get my GMAT score up apparently though...