Thanks for your responses.
The two containers stand side by side with about a metre between them. The are oriented north south, so one sees more of the westerly wind and the other the easterlies.
We've checked for rain ingress and there is no obvious sign of leakage. We did repair a few holes over the summer, in both containers, with adhesive lead flashing and then repainted the tops, so I'm pretty confident that they are watertight.
There are rubber seals around the doors which are in reasonable condition, but probably not airtight.
There is no compost currently stored in either container, but the dodgy one has quite a bit of timber while the other has none. A small quantity of bagged compost may have been stored over the summer, I can't recall now which container was involved.