Well, I've partially solved the problem, I think. I was completely unable to track down the guy who ran the company which technically owns the domain name, so I called Nominet directly. They charged me £94 to renew it, which is a damn sight more than the £5 they charge ISPs! In about 24 hours it should be working again.
The situation seems to be complicated by the fact that the company in question no longer seems to exist, having been legally dissolved at some point. As a result, Nominet will no longer accept the authority of anyone but the solicitors handling the affairs of said company to effect a transfer of domain ownership, which is undoubtedly going to make life difficult. I'm still not happy.
pca
_________________________
Experience is what you get just after it would have helped...