The bike has a 42 tooth chainwheel, 16 tooth sprocket, 100+ tooth chain. I think we can agree that the chain will be 'shifting' on the chainwheel and sprocket, i.e any given link in the chain will not consistently meet the same tooth on the chainwheel and/or sprocket. The chain is however tight at the same spot on every revolution of the chainwheel.
I tend to agree that the problem is therefore with either the sprocket or the chainwheel.
The bike has always been like this, even though I have changed the sprocket a couple of times, and regularly change between freewheel (commuting) and fixed (weekend), so I and tending to doubt that chain wear is significant (it may well be contributing).
Thanks for all the thoughts. They are really interesting.