London tap water varies a lot in different parts of London. When I used to live in North-West London it was very hard (ie: full of minerals) so you'd constantly be cleaning the limescale gunk out of your shower, off your taps, etc. And I also remember it smelling noticeably "chlorinated" at times. Now I live in East London (E14) and it seems much softer - we get a bit of limescale but nothing like it was at my old place, and no pool-water smells.

But anyway, I think anywhere in London, so long as you run it through a filter (ie: Brita filter) and chill it, it tastes more or less as good as any bottled water.