Abdy was baptised on 18 May 1612, and educated at Trinity College, Cambridge, to which he was admitted in 1629 as a Fellow Commoner.

Abdy married Mary Corsellis on 1 February 1638 at St Peter le Poer, London, by whom he had three children, James (b.

Abdy inherited the family seat of Felix Hall, Essex, upon his father's death in 1640, and was created a baronet in the following year, on 14 July 1641.

In 1651, Abdy was named High Sheriff of Essex, but continued to prosper after the Restoration, seeking a lease from the Crown soon afterwards of the sugar duty.

He inherited the property of his cousin Sir Christopher Abdy of Uxbridge in 1679, the same year in which his wife Anne died, on 16 June 1679.

Abdy died on 14 January 1686 and was buried at Theydon Garnons, Essex, being succeeded by his son Anthony.

Dr. Richard Milward, on 9 June 1682, by whom he had thirteen children: Thomas (d. young), Joanna (1686–1765), Elizabeth (b.

He was buried at Kelvedon, where his monument was designed by Edward Stanton, and was succeeded by his son Anthony Thomas in the baronetcy.

By his second wife, Charlotte Barnardiston (d. 19 February 1731), daughter of Sir Thomas Barnardiston, 3rd Baronet, he had one daughter, Charlotte, who married John Williams, son of Sir John Williams, Lord Mayor of London.

He entered the service of the East India Company and served as a midshipman aboard the True Briton from 1750 to 1752.

He afterwards transferred to the Royal Navy, and in 1761 he was made captain of HMS Beaver, a 14-gun sloop which had been built that same year.