It was only a flat battery. Well, a battery, one cell of which had died totally. The reason, said the AA man, was that I use the car too little, and allow the battery voltage to drop too low. I leave it for weeks at a time, several times a year, and even when we're living in the marina, it often doesn't get used for over a week at a time. So what happens, I was told, is that the plates in the battery cells develop deposits of sulphates, and these can eventually cause a short circuit between adjacent plates. This is what had happened to one cell in my battery. Time to get a new battery.
Mr AA man jump-started the car and left it with a charging pack for ten minutes, after which I took it for a spin to charge it more. The car would restart and drive several times that day, he said, but it'd be useless the next day. I checked on the web, and found that the Rugby branch of Halfords had a battery in stock, so I drove over and bought it, and fitted it there.
The AA guy also told me that the way to prevent damaging the battery through under-use was to buy a car battery solar charger to keep the battery fully charged all of the time. The AA had these on special offer on their website, so I duly ordered one, and await its delivery.
Thank goodness for these rescue services!