City water ("mains water" in British parlance) is classed as safe to drink everywhere, but subjective quality varies considerably.
There are localized pockets of variation as you would expect, but as a rough guide water is very hard in London, the southeast in general, and East Anglia. Parts of the midlands and north also have hard water. It tends to be much softer in the west of England, in Wales, and in Scotland.
Unfortunately, some districts are still running with antiquated distribution systems and the water companies tend to chlorinate the supplies more frequently as a safeguard. The water where I live, for example, while extremely hard is still quite palatable. Five miles away in town it's coming from the same source yet they chlorinate it so often that it tastes awful.
That limescale is a big problem here in eastern England though.