Have you contacted Jigsaw, the organisation that helps connect adopted people with their natural parents?

Have you contacted Births, Deaths & Marriages? If your father's name is on the original birth registration, they may be able to help you with information on how to take the next step. I doubt they would just cough up with the data, but they will know how you can get permission to see it, I expect.

Hope this helps. :-)

Kind Regards,
Wendy