it was the responsibility o the parent or parents to register a birth before 1875, and people didn't use the systen consistent;y, after 1875 it was the responsibility of the registrar.
anyway, you need to actually contact the register office that you think would cover the birth registration, sometimes errors and omissions were made with the national index.
If no luck with that, try looking for a siblings registration.
also. if his mum was not married to his dad, she could not register him in his dad's name, only her maiden name. have you checked under that name?