Am I eligible for UK citizenship?

[Myholland5]

My father was born and raised in the UK and at 28 years old joined the US navy becoming a US citizenship and married my mom (American) in 1988 and having me in 1990. Am I eligible based on his previous citizenship? My sister (a different mom than I) and all of my dad's siblings still live there and my grandmother who just passed lived there her whole life.

I have a copy of my dad's British birth certificate and his naturalization papers.

 

[Myholland5]

I forgot to mention, my grandfather, the paternal side was also in the US navy but he was an American. My dad states he never lived in US until joining the US navy.

 

[Riley Haas]

You can apply for a UK passport right now, with your birth certificate listing your father's name, your parents' marriage certificate, and your father's UK birth certificate.