... Oxbridge are weird. London is expensive. ...
True, but both of them also tend to have a very high profile in many science and technical subjects (I haven't got any idea about the fluffier stuff).
Looking at the Wikipedia entry for
Academic Ranking of World Universities (for example), the UK universities listed in order are Cambridge, Oxford, UCL, Imperial, Manchester, Edinburgh, King's College London, Bristol, Nottingham, Birmingham and Sheffield. So, the top four places are Oxbridge or London (with another London university a bit lower down).
Now, how fair, or reasonable these sort of rankings are, is another question, but people (prospective students, their parents, and more importantly in this context, employers) do look at this sort of thing.
Whilst engineering has a lot of maths in it, it's a lot less than something like Physics. So, if maths is a problem, you probably don't want to look at Physics! Computer Science is always a bit of a interesting subject, because people think that because they're interested in programming, they should be doing CS, but the maths content is, as has been mentioned, substantial.