Their problem with a British passport may be that although it's evidence of British citizenship, it
doesn't actually confer Brtish citizenship. They apparently want your original registration certificate to confirm that they didn't issue your passport in error. This says a lot about their apparent lack of confidence with their verifications in the past 24 years! Moreover, they
should give cogent reasons for their doubts.
However, if your wife has the original document granting ILR or confirming PR, then this may satisfy them. Does your wife have ILR under the Immigration Rules or PR under the EEA regulations? The grant of ILR actually confers her settled status. They may have a hard time
disputing the original document, irrespective of how she obtained it.
This is not intended to be legal or professional advice in any jurisdiction. Please click on any given
links for further information. Refer to the source of any quotes.