Having put the old chain back on, I get frequent skipping on the smallest gear and much less frequent on the next one up. Moving that link around has not changed this; unsurprisingly since it looks exactly symmetrical.
So suddenly the bike has become hard to ride. So I am going to change the whole lot now (cassette, chain and the front gear). Not sure I have all the tools needed so could be off the road for a while while waiting for stuff to turn up. Is there anyone near Brighton who could help if I get stuck, for some £££?
But I wonder what the cause might be of the old chain suddenly skipping. The only other thing I did was to remove, clean up and replace the two derailleur gears. Their bearings seem ok but I wonder whether a slight wobble (in the upper gear, which directs the chain onto the appropriate cassette gear) might cause chain skipping? I can get new ones; they are not expensive. They have ceramic bearings which don't need lubing.
Sometimes some patience allows such problems to go by themselves.
At the moment, the wear states of the individual drivetrains parts are different, but further wear will bring them back in line, since the surfaces that mate with other, will wear, and those that don't mate, won't.
The result is that gradually more teeth again start to share the load, reducing the load per tooth, and thereby stopping the skipping.
A file (alu) or an angle grinder (steel), may accelerate the process, but you need a good eye and watch out to keep it good.

And bonus: the patience solution doesn't cost bucks.