The registrar will have put on the certificate whatever surname they were told to put, if they put one at all. Till quite recently, UK birth certificates didn't even have a space to list the baby's surname. The registrar wrote down the full name of the father and mother, and also the maiden name of the mother, and the personal name(s) given to the baby: this could be left blank if the baby had not yet been named at the time of registration. Officialdom used simply to presume that if there was a father named on the certificate, the baby would have its father's surname.
And if a birth certificate did have a space specifically for the child's surname, it would be up to the person notifying the registrar of the birth to say what that surname would be.
If a man had changed his name, for whatever reason, I can't imagine his deciding to give his child the surname that he himself had jettisoned rather than his new one.