British father changed his name before I was born

[giraffe]

I am Australian. I was born before 1983, my father is British, and my parents were married at the time of my birth.

Correct me if I am wrong, but I understand that makes me British by descent according to British nationality law.

But how do I prove it?

At some point in his childhood, his name was changed by deed poll. So basically, the name on his birth certificate is different to the name on all his Australian documents, including my birth certificate.

Unfortunately, I gather that obtaining a copy of deed poll can be extremely difficult. He's not exactly sure what age he was when his name was changed (he was very young), and he's not exactly sure where he lived at the time (he moved around a lot).

What other documents would be sufficient for me to obtain a British passport?