He had gained a degree of notoriety as a bigamist after his marriage in February 1744 to a wealthy heiress, Miss Anne Warneford, granddaughter and eventual heir of Sir Edmund Warneford of Sevenhampton and Bibury, Gloucestershire.
Anne had married Cresswell in good faith and had borne him two children but another woman, his cousin Elizabeth Scrope, sued on the grounds of bigamy, claiming a prior Fleet Marriage.
Miss Scrope's suit was successful, the Cresswell–Warneford marriage was declared null and void, and the children (a son, Estcourt, and a daughter) were bastardised.
[3] Cresswell had at least another four illegitimate children with a Miss Catharine Jenkins between 1749 and 1755, the three survivors of whom received substantial bequests from their father on a par with their half brother Estcourt, who was MP for Cirencester from 1768 to 1774.
A fictional account of some of these events is given in "Love and Avarice: Or, the Fatal Effects of Preferring Wealth to Beauty" by a 'Lady of Shropshire' published in 1749, in which Cresswell is Clodio and Anne Warneford Leonora.