Another update. I have managed to get the backs of the rear seats out and the covers fitted. Thanks to the Dutch video I realised it was possible to tuck the vinyl under the plastic fittings for the head-rest mounts and get a much improved look (also access to the wee button that lets you change the height). I also saw that he had tried the same trick with the mounts for the levers that let you fold the back seats, but the holes cut in the vinyl for these fittings have fabric piping stitched round them and this got in the way and wasn't so neat. He also said it was hard work.
So I got out the scissors. I snipped the stitching and removed the fabric piping. Then I realised I had to enlarge the holes a bit, and in fact cutting round the line of the stitching holes was about right for the levers at either side. The centre seat belt fitting needed a bit more cut out, but it worked very well. The end of the zip tucked neatly under the plastic fitting, whereas before it had been sticking up rather awkwardly. This photo is of the top of the near-side (larger) rear seat back piece, lying in its back in the load bed, before I re-fitted it.
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Admire. And then do likewise. (I can see it's also possible to do the two holes on the back that allow access to the child seat anchor point, but I didn't bother because they aren't seen. I might do it later though, as it could easily be done without taking the seats out again.)
I put the seat backs back in position because I don't think they need to be out for the seat itself to come out. The only minor snag is that with the extra material there, the seats don't fold as easily as they used to. I now find it best to unclip both seat backs and line them up, before shoving them back into their clips as a unit, to get the covers to lie neatly.
I have not yet succeeded in getting the seat itself out, and neither did my neighbour, even after watching the videos above. The car is however due in the dealer's on Monday and I'll ask them if they can remove it for me. (If it's my lucky day they might even fit the cover and replace it, but even if they don't, I should be able to manage if they get the seat unclipped, with my neighbour's help.)