Hi Tim Tracker,
Yes I found the whole thing bizarre too: the birth for the same person registered twice, 23 years apart, had me completely baffled. Both records were for the same person; dates, parents names, everything exactly the same.
However, I have since discovered that if the parents of a child marry after the birth, they can request to re-register their children under the married name. The new certificate is completed on the authority of the Register General, which these were.
I had originally presumed that my grandparents had been married at the time they begun having children, but I was never able to find any evidence to support this theory. Therefore I delved further.
I found a marriage record for my grandparents in Jun 1972, just days before the recorded date on the birth certificate. I also discovered that each of their children had two birth certificates: one in their mother's name and one in their father's name - with one exception - their second eldest son had died a few years previously to 1972 and therefore could not be re-registered (as the child must be living to be re-registered.
The only puzzles I have left to try and solve are, why my grandparents waited so long to marry and why they re-registered the births when all of their children were grown. I guess that it was that important to them.