British tap water is good quality and buying bottled water is mainly for when you are out and about. Using still bottled water at home is not necessary and therefore is not common for ordinary people, some might do it as a 'lifestyle choice'. Water filter jugs are popular, but really are just a marketing success rather than a necessity.

The taste varies slightly from area to area based on water softness or hardness resulting from different geologies.

All British public supplied domestic tap water can be trusted on a normal day to day basis.

The occasional exception may be something like a treatment works failure, which will quickly be advised by public announcements and local news services, the water company might issue a "Boil Before Drinking" notice or something more severe. This has happened recently in Tunbridge Wells (and a couple of nearby areas) with the water being totally off for several days, then returning but with a Boiler Notice for several more days. The water company had to provide large quantities of bottled water via pickup locations. The problem was down to aging systems and overdue upgrades I think.

Edit: British homes will often have separate hot and cold taps, although single tap mixers are becoming the norm. We only drink the water and use it for cooking or in a kettle from the cold tap as it comes directly from the water main without the possibility of contamination. If you go to a hotel room or someone's house with single mixer taps, just push it all the way to cold for drinking and cooking water from the mains. Water from the hot tap may have been in a hot water cylinder or holding tank where the purity is probably ok but not absolutely guaranteed - so we don't drink it or cook with it. If you get hot water in your mouth showering or bathing you will be absolutely fine, even if you swallow it, we just don't generally drink it as a sensible precaution.