Well consultancy is always orientated to the clients but management consultancy solves very different problems to technical consultancy.
Management consultancy is generally asking how a company change change/develop/re-strategise focusing on the commercial outcome, and often they come in to businesses that are in a negative position i.e. decreasing market share/revenue stagnation/no longer profitable... and they will come in and advise very difficult decisions.
technical consultants tend to do a variety of stuff which can either be purely technical advisory/strategic/commercial advise with a general focus or depth of understanding of the technical issues, they sometimes work on really long term stuff (for example understanding what the stepping stones are so that you can be competitive in X number of years if Y technology becomes available) or they can advise on urgent technical scenarios which need an answer in 30 or 60 days, there is very wide scope.
Management consultancy tends to involve more travel i.e. you will regularly be at clients sites 4 days per week and you will be flying/travelling constantly. Technical consultancy travel varies, sometimes you could be seconded to a client for a couple months and other times you can work from home/office for long periods of time. Id say technical consultancy probably has more "normal" days but being flexible is part of the nature of consulting.
As for alternative universities to UCL, id highlight my previously listed unis. Id note if you do wish to target MBB careers id probably go with prestigious unis perhaps, Bristol. MBB is very competitive (less then 1% of applicants receive an offer at McKinsey, bain & BCG are about 2% - and lots of people who do enter these companies don't make it in as graduates but either after an MBA or applying with 2,3,4 years experience).