Am I British if my Dad was born in the UK?

If your father was born in the UK before 1^st January 1983 and he was not a diplomat working for a non-UK country or your father was ‘an enemy alien in occupation’ he would be a British citizen otherwise than by descent and in turn his children may be British citizens permitting certain requirements. If your father was born in the UK on or after 1^st January 1983, he would be considered to be a British citizen otherwise than by descent as long as his parents had the right to live permanently in the UK at the time of his birth. He would be able to pass on his nationality to his children permitting certain circumstances.

Read more about this here.