A shocking state of affairs.
A simple solution would be for all such inquiry websites to be at example.gov.uk or example.justice.gov.uk - then, if there really is a good reason not to maintain them, they can be redirected to the home page, http://www.gov.uk - or to the National Archives' version of the site.
Local government is no better. When I worked for Birmingham City Council, I found that the council had over 100 websites (including registered and unused, or lapsed, domains) other than the main one. Many were unmaintained, or not adequately maintained. Several involved paying external providers to replicate services already available corporately. One even displayed the defunct mobile phone number of a former staff member, in whose name - as a private individual - it was registered, and whom we were unable to contact. Some of the URLs were on promotional goods such as rulers, cups, keyrings and bags, whose expected lifetime exceeded that of the defunct website.