Just to update...
I pulled out the cap, and saw that it's a mess of cracks all round. It's one of those old Rifa paper caps in a yellow plastic casing and, well, I think it would be a little unfair to expect it to have lasted 40 years
It's marked 0.22uF (250V~), and I measured it just out of curiosity and it came out at 0.32uF... but kept flipping to zero. So it's obviously shorted. I've replaced it with a 0.22uF polyester (305V~).
While I was there, I noticed the motor suspension belt was looking a bit ragged, and the rubber on the feet was starting to harden, so I replaced those too.
It's all back together now, and playing great
Tonally it's defintely better too - particularly noticeable in the upper bass, which is cleaner and more defined now where it used to be a bit woolly.
Anyway, with new lube and new drive belt too, I reckon it's good for a few more years now.
So thanks, Andy, for the tips.
Alan