I got an Irish passport in the 80's, because when I was born in The States in the 60's, my father, who was born in the states in the teens was already (automatically) an Irish citizen because his father was born in Ireland in the 1880's. My grandfather died in 1919, and my father has not lived in Ireland since 1921. My father does not recall ever having an Irish (British?) passport or any other document showing his Irish nationality.

Was my father ever a British subject? Before 1 January 1949? He doesn't recall having a British passport, but he lived in Ireland for 15 months when he was six.
Could I get a British passport?

I mean, I already have an EU passport so why would I want another one, right? But, I have always been curious about this.