It's amazing how much fuss one disintegrating washer can cause.
It turned out that the rubber washer in the house stop tap ② had fallen apart and the bits whooshed along to the kitchen sink and header tank.
Here's what happened, over the course of a few weeks:
The water pressure in our kitchen sink was low and the header tanks upstairs weren't filling properly. I could see that the flow into the header tank was poor so I surmised that something was blocking it up - possibly some grit? I thought I'd investigate, so I went to turn off the stop tap that's inside the house ②. Uh-oh - it didn't turn off the water fully. When I looked up diagrams of how stop taps worked, I guessed that the washer inside might have disintegrated.
I went to turn off the outside stop tap ① - that didn't work either! Double Uh-oh!! Our water supplier is United Utilities and they acted very promptly to get that stop tap sorted: someone came to have look the next day - and the day after, the tap was replaced with a new unit. Thanks, UU!
Our header tanks have float valves eg at ⑤. When the tap is run in the bathroom, the water level in the header tank goes down, the float goes down and the action opens the valve to let mains water in. When the water is full again, the valve will have switched off. If for any reason the valve doesn't switch off properly, there is an overflow pipe to let excess water drain away outside.
With the water supply safely off outside, I was able to investigate the float valve, I found some bits of washer bunging up the inlet, reducing the flow into the valve. Once this was cleared the flow returned to normal. You can see the valve in the photos including the view looking down the inlet together with the bits of washer removed.
I've just remembered that there was a problem with a second header (not in diagram). For this tank, the float valve was not shutting properly when full so a little excess water was going through the overflow. In this case, the problem was a piece of washer getting stuck inside the valve so it wouldn't shut off properly.
While the water was off I checked out the kitchen sink. There were two problems there: there were bits of washer stuck with the taps at ③ and the end of the tap ④ has a strainer which was clogged up. The main problem was the grot accumulated at the strainer at the end of the tap, which I could have removed easily without dismantling the tap.
Finally I was able to think about the inside stop tap. I was wondering about replacing it completely as it must have been there quite a while. However it joins old black mains water pipe to 3/4" copper which then changes to 22mm copper. The whole caboodle is probably very set in its ways, and there's very little black pipe to play with. If a replacement went wrong, I'd have to dig up the floor and the concrete outside to update the supply pipe. That sounds like too much fuss.
Luckily stop taps can be taken apart. Ours was not for turning - until I'd borrowed a blinking big spanner. As expected, the washer was missing from the inside. Once I'd got an ordinary 1" tap washer replacement, it went back together a treat - and worked! Whew - what a palaver!