I contacted the registrar, Yell, and was told that their policy is to renew domains even if the customer doesn't choose to pay for them, in case they are needed in future. When I pointed out that this was a bit daft if the customer no longer existed, they referred me to Nominet (the central organisation that looks after domain names).
Nominet said that they could only cancel the domain (so freeing it for re-registration) if they had tried to send a letter to the address and it was returned as undeliverable. This seems unlikely to happen. I'd have thought most businesses would just bin the letter if it was addressed to an organisation that had vanished some time previously.
It seems like this domain has become a ghost, doomed to be renewed forever and never used!