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.

But aren't you the nominal owner of the domain? The ISP should only be the tech (and perhaps admin) contact, but you should have the formal ownership of the domain!