It's been a long time but I wanted to return to this old thread to tell you all what happened in the end. Haven't had a chance but now I've been furloughed from work there's no excuse!
It turned out that the adaptor plate that the PO had made to fit the flex plate had disintegrated, it was thin gauge metal and must have been flapping away for a little while before giving up the ghost entirely:

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My local Morris garage no longer have anyone who can machine parts, but Steve Phillips of this forum came to my rescue, and made up a much sturdier looking flexplate which fits perfectly:

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Peggy now drives much better than before with a bit more power; apparently the prop shaft is a little too short and has a shim making up the difference, so getting it lengthened is on the list of things to sort once this craziness is all over, hopefully that'll give a little bit more power to the wheels as well. Since then I've been carrying on with the endless list of little jobs; getting the wipers to work both fast and slow, replacing the plywood boot floor which had rotted, caulking the back windows, touching up the paint, adding electronic ignition (which has transformed the performance, I think the old points were on the way out). I now have a couple of new little problems though, which I'll put in a new post!
We had some decently long drives out before the virus descended, down to West Sussex and back, and over the North Downs to Kent, including some tiny lanes, steep hills and unexpected watersplashes, but she performed faultlessly; to conclude, here's a photo of her outside the George and Dragon in the village of Downe:

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