A bit surprised he isn't on BCC.
All of the accounts of him say he was born 1805, Oakham, Rowley Regis. He spent several terms in jail for various minor crimes (including abandoning his wife and family. It was while he was in Stafford jail that his career as a hangman began - he volunteered when William Calcraft found himself without an assistant to perform a hanging. Most accounts also mention that he had a son George, who assisted him at some of his hangings.
George Smith was famous as the man who hanged 'Palmer the Poisoner'. There have been a number of articles in the 'Black Country Bugle' about George Smith (and also William Palmer).
I think these are the baptisms of George Smith and two brothers:
Samuel SMITH chr 28 Dec 1794 Rowley Regis - parents: Thomas SMITH & Francis.
Charles SMITH chr 9 Apr 1797 Rowley Regis - parents: Thomas SMITH & Francis
George SMITH chr 27 Apr 1806 Rowley Regis - parents Thomas SMITH and Frances