I'd basically echo what Miya said. With regard to reputation (domestic and international) they are both virtually identical. I'm sure that the options offered are pretty similar for the most part and besides, there won't be any objectively better set of options. It will all be based upon what you find more interesting.
The only really distinguishing factors have to do with location. While Nottingham has the benefit of both a campus and large city nearby I just don't think it can really match London, in many different respects (apart from cost of living...). London has pretty much everything you could ever want with regard to art, culture, entertainment, etc. I would normally make the point here, that as KCL is in London you are near to all of the big city firms and so can just hop on a tube-train and nip along to their offices for interviews at very little expense, both financial and with regard to time. However, if you are planning on going back to Singapore to practise, this point is essentially null and void.