The UK has no notion of a person number or national ID number that is tied to citizenship. Therefore it is not possible to prove British citizenship except with a British Citizen passport, naturalisation certificate or pre-1983 birth certificate.

It’s therefore a lot harder to prove citizenship for an initial passport application in certain circumstances than you might expect. You need to prove that you have an unbroken link of people born in the UK to someone born before 1983, and as time goes on that will mean even more generations. Right now you typically need to provide your birth certificate, up to 2x parents birth certificate, and up to 4x grandparents birth certificates.

In many other countries the birth certificate will have the person numbers of the parents, which will mean there’s essentially guaranteed to be a record of the citizenship of the parents that the state can check. Alternatively there’s a national ID scheme that helps bootstrap this information early in life.