What does the "non-drinking water" sign indicate about water quality in the UK?

Commonly in the UK, cold water may be stored in open (or roughly covered) tanks in the roofspace.

Such water, while it will have been drinkable mains water when it arrived is considered non-potable as there is no knowing what might have contaminated it while sitting in the tank.

Contrary to the other answer, it is very unlikely that grey water is coming out of a tap, though untreated water is another possibility in rural areas.

See https://www.theguardian.com/notesandqueries/query/0,5753,-2404,00.html for thoughts on why this system exists. (A classic Fawlty Towers episode sees the hotel inspectors find a dead pigeon in the hotel water tank.)

Whether this is the case in every instance is debatable.

It is a requirement of the Health and Safey Executive that water is marked as "Not Drinking Water" unless it meets the requirements to be considered drinking water.

Drinking water

An adequate supply of high-quality drinking water, with an upward drinking jet or suitable cups, should be provided. Water should only be provided in refillable enclosed containers where it cannot be obtained directly from a mains supply. The containers should be refilled at least daily (unless they are chilled water dispensers where the containers are returned to the supplier for refilling). Bottled water/water dispensing systems may still be provided as a secondary source of drinking water. Drinking water does not have to be marked unless there is a significant risk of people drinking non-drinking water.

Should water in a particular supermarket toilet come not directly from the mains supply but via a storage tank of some kind between the mains and the toilet it would not be considered drinking water.

The important thing to know about drinking water, in the UK and everywhere else, is that, while it leaves the water treatment works in a disinfected, safe, state, it then has to travel through many miles of pipework before being consumed. It is impossible to keep this pipework completely clean and so the water is treated with a disinfection agent such as chlorine (traditional solution, but can affect the taste of the water) or chloramine (used more often nowadays since it has less taste) that stays in the water and keeps it safe for a period of time, typically 5-7 days depending upon the strength and chemical used. The water distribution systems (the pipes under the streets) are designed such that the water will reach the consumer well under this time period and so be safe at the point of use.

In a domestic situation, where the kitchen tap, the primary source of drinking water, typically runs direct off the water mains, this is safe. In large commercial buildings however, there is a large amount of additional pipework, extra storage tanks, pumps, etc. and in order for the water to be guaranteed safe (it's not ok to be alright most of the time) all of this additional infrastructure must be periodically flushed, disinfected, and tested in order to ensure that no pathogens can be introduced into the water. This is an expensive hassle and so the simplest thing to do is to have a separate, simple, drinking water supply within the building, which does get cleaned and tested regularly, and to label all other water points as non-potable.

You probably won't get ill drinking from such water points (due to the presence of existing disinfection agents and engineering safety factors), but is it really worth a dose of the squits?