Wheble was apprenticed in 1756 to "the well known bookseller, and publisher", John Wilkie, whom he eventually succeeded.
Wheble is most famous for his association with John Horne Tooke and John Wilkes, and the Society of Gentlemen Supporters of the Bill of Rights, having printed pamphlets for them, and publishing articles in "The Middlesex Journal" in their defence.
A proclamation for him to appear in Parliament was also made in the name of King George, with a reward of fifty pounds offered for his apprehension.
In his letter to the Secretary of State, Lord Halifax, Wilkes wrote "That Wheble had been apprehended in violation of the rights of an Englishman, as well as of the chartered privileges of a Citizen of London" For his services in these affairs Wheble was granted 100 guineas by the Constitutional Society, and received the thanks of the Corporation of London.
He was the projector of "The Middlesex Journal" and "The County Chronicle," and with Mr Harris co-founded "The Sporting Magazine."