Hi Philj,
Although there are clearly many factors to consider here, personally, I would go with the supervisor.
I was in a very similar position to you - from Australia, moving to the UK, had offers from 'top' schools and good-but-not-the-most-internationally-recognised schools with people I really wanted to work with. I'm in a sort of similar field to you as well.
I had known other people in similar situations who had chosen to go with the 'best' school and had ended up regretting the choice, so after a lot of consideration I decided to go with the supervisor I wanted to work with the most and it's been the best decision I could have made.
Another thing I want to point out is this - don't discount the fact that in some places (you mentioned UoL colleges, and I'm thinking of this in particular) the 'main' postgraduate community can be based outside of the university/college and incorporate a lot of different schools and people from different programs. I have found that to be a wonderful, rich and supportive academic environment which I think has given me access to a lot of ideas and perspectives I may not have had otherwise. So - if you're looking at going to a UoL college, check out the Advanced Schools and their programs as well.
Good luck with the decision.