If the birth was registered, then it should be shown as an addendum on the appropriate page of the GRO Index. My grandmother b1872 Cambridge had exactly the same problem when she wanted her pension, no birth certificate, only she said that her birth had been registered and that the registrar at that time was an alcoholic, he would take the fee, tell the illiterate person the birth was registered, and then pocket the fee without issuing a certificate. A nice little earner on the side!More seriously the registers at Thame should have been transferred somewhere when the office closed, and should still be available.