Thanks RocketMan, I had wondered what might be in that part of the unit and what you say about condensation and pipework makes sense.
I’ve just discovered a milk bottle at the bottom of the door full of white sludge. I was using the milk this morning and it was fine (it’s still well in-date). Now I have cheese.
If I wasn’t sure before, it seems certain this is a real problem rather than just the warmer edge of the operating range.
What could be causing this pipework to heat up so much? I’ll certainly check the things you suggest, but I think I’ll have to try to find a local engineer tomorrow.