Some years ago a Registrar in London told me that unregistered births occurred from time to time in the UK until 1948. Whilst before that there had long been a legal requirement to register a birth, there was no obvious immediate practical benefit to the parents and so occasionally people just didn’t bother. He cited illegitimacy as a common factor, though there could be other reasons. The behavioural change in 1948 came with the introduction of family allowance paid by the state. You needed a birth certificate to make a claim. As a result, from that time onwards people would nearly always register births promptly. Otherwise you wouldn’t get your money!
The Registrar told me that the Superintendent Registrar has discretion to register a late birth, even if that was 5 or 50 years later. However to do so, normally someone present at the birth (not necessarily the parents) has to be able to swear to the event, and explain why it was not registered at the time.
He added that usually the need to obtain a passport or a pension was a factor leading to the late registration.