John Wilkes did not marry the daughter of Queen Anne. He married Mary Sherbrooke Mead. Their daughter was named Mary "Polly" Wilkes. She had no children.
It is unlikely that you are descended from either of his 2 illegitimate children - Harriet Wilkes who married William Rough and moved to Ceylon or John Henry Smith, whom we have no record of ever marrying and who probably died in India.