Mine has had a very similar set of issues. It started when the car flooded due to a blocked drain below the windscreen during the pandemic. I dried it up, but found issues with one
fog light and the windscreen washer not working.
Fog light seemed to come good after reconnecting it a couple of times. But along the way I took all connectors apart including the white one and cleaned up. Nothing as clean as Mr Underhill's. I managed to get it so it wouldn't start too, but there was a trick with the key in the ignition and getting the car to re-recognise it that sorted that.
I checked every fuse in the car, including fuse box and under bonnet. Cleaned up and reseated all of the relays (including one which came apart when I tried to pull it out. Checks the earths, unplugged and re-plugged in the UCH a few times which seemed dry and clean (although there is something still holding it in place that I can't find so have not been able to actually get it out.
Washer motor is fine if I
hotwire it across the battery.
If I pull the stalk to test the washer (or twist the sleeve to also power the washer jet for the rear) the washer connector just gets a few hundredths of a volt. I beleive mine has just one washer motor to power the front and rear windscreen washers, but not sure if that's right. I checked a wiring diagram I found online and it didn't look like there was a relay between the stalk and the washer motor, but that may be incorrect.
Windscreen washer still does not work to this day...
I'd suspected it may be either the stalk or the UCH, but odd that both switches in the stalk would fail at the same time. Which leaves the UCH or a wiring issue. Or of course something I don't know about or have incorrect.
Watching intently to find the root cause on this chain!
Is that Diamond Motors in Croydon by any chance?