In the hope that it will help other people who have the same problem of a sticking tap, I would like to report what I eventually found out.
I replaced the washer a further two times, using a different make of washer for each replacement. The tap still stuck. On the final occasion, the tap stuck in the OFF position, and I could not by any means turn the water back on.
I removed the tap mechanism (again!) and inspected it. The rubber washer is mounted at the end of a hexagonal rod (the male piece) which, by screw action, moves up and down inside a hexagonal channel (the female piece). By this means, you can turn the water on and off by turning the tap handle.
In my case, the male piece had become damaged so that it no longer moved freely up and down the female piece. Hence the sticking tap. The only way to rectify it was by buying a new tap mechanism. In my case, the plumbing store did not have a mechanism that exactly matched the one I had removed, so I could not fit the old tap handle to the new tap mechanism. For that reason, I had to buy a pair of tap mechanisms, including appropriate handles of a new design. To make the two taps match, I had to fit the new mechanisms and tap handles to the hot tap as well as the cold tap.
One tip:- If you need to disassemble a tap mechanism for inspection, remember that the screw retaining the tap-washer back-plate has a left-hand thread. The reason for this is obvious if you think about it (which I did not, for some time of futile effort).
The damaged washer, which I found at the beginning of this saga, turned out to be a red herring. I suspect that the hexagonal male piece was damaged when people turned the water off with excessive force, trying to compensate for the leakage caused by the original faulty washer. Only to this extent was the original faulty washer involved in the problem I was trying to fix.
Richard Chambers Leeds UK, November 2016
