How to define 'in London'?
-You could say all places on the tube network.
-You could say all places which are covered by a London Borough.
-Or you could say all places which have a London postcode, namely N, S, E, W, and combinations of the two.
If you really want to be in the centre of things, then go by the postcode. So, Brunel is in Uxbridge (yuck) and has a 'U' postcode, therefore not London (and I did politics there, and wouldn't necessarily recommend it)
Looking through the list of UCL colleges, Kings, LSE, SOAS, SSEES, are smack in the middle of London. Royal Holloway is in Egham, as said, which is lovely but a bit of a pain transport wise, and quite insular (Brunel used to have a campus nearby but it closed down), Queen Mary is in Whitechapel, which is fairly central though more East London, which is quite trendy these days, and Goldsmith's is in New Cross, which is very East and REALLY trendy right now.
Others are University of Westminster, University of East London, but LSE and other UCL colleges are old and will be much better in terms of rep.
Vicky