Can I get a UK Passport?

pologising in advance if this has been answered somewhere, but I've searched the threads and only came up with this, which leads to my question:

You may have had citizenship of the United Kingdom and Colonies by descent from a father who had that citizenship, or because you were registered or naturalised as a citizen of the United Kingdom and Colonies.

My father was born in England. He moved to USA as a young man. Became a US citizen but did not renounce UK citizenship.
Does this mean I have British Citizenship?
I want a British passport. Can I apply for the passport by proving the above, without applying for citizenship? I'd hate to pay for both processes if I don't need to.

Sorry to be so dense on this but it seems way too easy.

you are most likely already a british citizen by descent but just to make sure...

1)how old are you?
2)were your parents married at the time of your birth?

What is your birthdate?

I was born in 1946.  My parents were married.

then it would be my understanding that yes, you are a British citizen because you had a British father who was married to your mother at the time of your birth.

(eta: just as an interesting sidenote, if it had been your mother who was British, you would not be a British citizen because women couldn't pass on citizenship in 1946.  But since it was your dad and your parents were married, you're British!)

Yay!  So I guess just need to prove this to the passport agency?

Originals or cerified copies I assume.
Daddy's birth cert.
My parents' marriage cert.
Daddy's death cert.
My birth cert.

ETA Thank you