I would certainly second Malishi - I've raved about it on here before.
However, it may be in danger of becoming a bit of a victim of its own success. The two times I've been, I waited between 30 and 40 minutes for my appointment, in one case because the previous two appointments had both run late, and in the other because the person before me had booked a cut and blow dry and then changed her mind and wanted colour too.
Normally that wouldn't bother me, but I was trying to get my hair cut over lunchtime and it was a bit frustrating. I would probably only book on a Saturday or when I have an afternoon off now. The cut in both cases was, however, still excellent.
I go to Bridges (I think) on St Thomas Street opposite Guys hospital. Despite my rubbish descriptions, they seem to get my hair right every time. Gina has vision! The colours she suggested looked wonderful the first time I went, so I went back again. I will return there as soon as I have the cash to go again. My roots are shocking at the moment... No connection, incidentally. Just a very satisfied customer.
I used to go there, but they are quite expensive, very slow (4 hours for a semi-permanent colour!), and they always got the colour somewhat wrong (too light / too dark / no movement in the colour). And they didn't seem concerned enough about getting drips off the skin before they marked. When I was having a permanent colour, this was a problem!