Family History of Smith

I am researching the history of the Smith family in Rye.

William Smith (b. 1716) and his wife, Elleoner, had a son named Jeremiah Smith (b. 19 October 1734, d. 1760). He later moved to South Carolina where his son, also Jeremiah Smith (b.1755, d. 1827), was born.

I am trying to find out who William and Elleoner’s ancestors were. William was born in Battle, East Sussex and Elleoner was born in Rye. They lived in Rye and that is where the first Jeremiah was born. Unfortunately, I don’t know Elleoner’s maiden name.

Any help would be greatly appreciated.

Thank you