The son of Sir John Ingilby, 1st Baronet and his wife Elizabeth Amcotts, he entered the House of Commons as Member of Parliament (MP) for East Retford in 1807.
In the same year, he succeeded his maternal grandfather, Sir Wharton Amcotts, 1st Baronet, in his baronetcy by special remainder.
Ingilby left Parliament in 1812, and succeeded his father as baronet in 1815, inheriting Ripley Castle in Yorkshire and Kettlethorpe Hall in Lincolnshire.
He held that seat until the abolition of the constituency in 1832, and he then sat for North Lincolnshire until defeated in the 1835 election.
Amcotts-Ingilby, a very eccentric character, was twice married, but left no children; his baronetcies became extinct upon his death on 14 May 1854, at 23 Abingdon St, Westminster.