Chesired5, you've really helped me to get a handle on the problem. Thanks.
I managed to get a look at the compressor while my wife started and stopped the AC. Short video here:
https://1drv.ms/u/s!Ao8CBdf9s4C6jlijb06OAsjnfxNR
That doesn't look like normal behaviour to me. It's basically freewheeling and occasionally catches briefly.
Also, I spot that black goo around the pulley. I suspect that's melted clutch material. And I suspect it is this that I smelled when everything went to pot, rather than electrical burning.
So my theory now is that after a longish drive on a hot day (almost 40 degrees IIRC) I parked the car for an hour to heatsoak then straight back onto the motorway. I think the clutch got really hot and melted and the alternator also chose that moment to hari-kari from the extreme heat. I don't think one took out the other, but rather that the heat was the common factor causing failure of both.
Looks like I'm in for a compressor change. I hope it's not as much of a nightmare as the alternator replacement.
Anyway, thanks everyone for your help.