He was educated at St. John's College, Cambridge and entered the Middle Temple.
He was not a very active MP, although he earned some praise for his willingness to sit in the Commons without wages.
The most memorable event of his life was when he accidentally killed a man during target practice in 1625, for which he received a royal pardon.
Romney Corporation was advised that it was entitled notwithstanding the pardon to seize his goods but declined to do so, as Godfrey, if not a very active MP, was personally well-regarded.
He was the great-grandfather of the noted writer Sir Richard Steele, through his eldest daughter Elizabeth who married Sir William Steele, Lord Chancellor of Ireland.