The British Nationality Act 1981 came into force on 1 January 1983. Prior to 1983, British nationality was only be transmitted from the father through one generation only, and parents were required to be married.
That can be construed as jus sanguinis or possibly even a type of lex soli in Obama Sr's case, but not jus soli (unless you want to give the Kenyan birth theory credence)
OBviously, Obama was not born in Hawaii, so the odds that he was born in Kenya are looking like a sure bet.
How many times do I have to say it?