Escourt was the son of Sir Edward Estcourt of Salisbury. He matriculated at Wadham College, Oxford on 8 May 1618 aged 17 and entered Lincoln's Inn in 1618. He was knighted on 6 December 1622 and created a baronet on 17 March 1627. In 1626 he was of Newnton when he became High Sheriff of Wiltshire.
In 1628, Estcourt was elected Member of Parliament for Cirencester and sat until 1629 when King Charles decided to rule without parliament for eleven years. He fought for the King in the civil war and was taken prisoner after the fall of Bath. He was assessed for a fine of £1000 but neither compounded nor paid the fine.
Estcourt married Anne Nordaunt daughter of Sir Robert Mordaunt, 2nd Baronet of Massingham Parva, Norfolk. He was succeeded in the baronetcy by his son Giles who was killed in duel in Italy. Estcourt's son William then succeeded but when he was killed in a pub brawl the baronetcy became extinct.
- 'Alumni Oxonienses, 1500-1714: Eade-Eyton', Alumni Oxonienses 1500-1714: Abannan-Kyte (1891), pp. 440-479. Date accessed: 8 July 2011
- Willis, Browne (1750). Notitia Parliamentaria, Part II: A Series or Lists of the Representatives in the several Parliaments held from the Reformation 1541, to the Restoration 1660 ... London. pp. 229–239.
- Basil Duke Henning The House of Commons, 1660-1690
- W R Williams Parliamentary History of the County of Gloucester
|Parliament of England|
Sir Neville Poole
|Member of Parliament for Cirencester
With: John George
Parliament suspended until 1640