So I posted a query on the support forum. Within a few hours I received a very comprehensive list of possible solutions from a community member called Timethief. None of the solutions worked for me, but Timethief asked for a bit more information and then tagged the issue for a staff member to pick up.
The next day a happiness engineer (what a great job title!) called Kartodim took up the case, suggested a couple of things, and after a few asynchronous clicks everything was back in working order.
I hesitate to call it customer service because all of this comes from a service that is free. Some of the other companies that I do give hard cash to could learn a lot from WordPress support.
I’m very impressed, in fact I’d say that I’m a raving fan – definitely five stars (according to my system).