Though where I live, even table water would be better than unfiltered tap water. Not because of health concerns (I actually had my tap water lab tested as the building is from the 60s), but because of limescale in the kettle and disgust on my tastebuds ;)
After the world seems to be in agreement that CocaCola and most lemonades are best served carbonated. But for water there's this weird schizm over carbonation.
It's interesting because the correct answer is that each country/region has different expectations from bottled water, mineral water.
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.