Born in Uganda '59 to British parents

I am attempting to acquire a British passport for my son. I was born in Uganda in 1959 to British parents. The family moved back to Scotland in 1963. In 1967, we moved to Canada. In 1976, I acquired a British passport from the British High Commission in Ottawa (Canada). In 1985, I acquired Canadian citizenship. My British passport expired and was not renewed. In order for my son to obtain a British passport, I understand I need proof of my British citizenship. All I have is my Uganda birth certificate and expired British passport. I do not have a copy of a naturalization document and an inquiry to the National Archives of UK failed to turn up a record of a naturalization document.

Do you know if I would have had a naturalization document and if so, where I could I apply to get a copy? Or, was my Uganda birth certificate all I needed?

Thanks for your help.