Finally got off my arse and bought a can of carb cleaner. Took off the valve to find I'd done a crap job of cleaning it the first time round.
The plunger had a black coating which I had to use very fine emery paper to get off, but now is all nice and shiny. I sprayed carb cleaner into the valve and later put some oil on the shaft as has been suggested by various people here. I also gave the carb body and mating surfaces a good squirt and scrub with a brush. Put it all back and now the problem seems to be gone. It idles from cold now which it would never do before, and the random overfast idling has been cured too. Marvellous.
I guess I shall have to see if it lasts - whether the problem was just dirt or the valve is pretty much goosed anyway.
Cheers,
Gareth.