Yes, I know the parents of William Bancroft.His father was Eli Bancroft, b. abt 1772 in East Windsor, Hartford, Connecticut, and d. 1830 in East Windsor, Hartford, Connecticut.He m. Polly Mason 7 Dec 1777 in West Springfield, Hampden Massachusetts.They had two children:William Bancroft b. 29 Jul 1802 in East Windsor, Hartford, Connecticut and d. 2 Apr 1861 in Tecumsah, Lenawee Co., Michigan. and Mary Bancroft b. 27 May 1804 East Windsor, Hartford, Connecticut and d. aft 1850. She married John Watrous.
Eli's father was Abner Bancroft, b. 30 Oct 1739 in Windsor, Harford, Connecticut and d 16 Aug 1816 in Windsor, Hartford, Connecticu.He married Sarah Bryant abt 1759 in Windsor, Hartford, Connecticut.I have traced the Bancroft line through Abner back to 1500 to William Bancroft, b. 1500 Chelaston, Derbyshire, England and d. 1557 in Chellaston, Derbyshire, England.He married Anne.