Drewe was born at Lezant, the son of Rev. Edward Drewe, canon of Exeter, and his wife Joan Sparrow daughter of Anthony Sparrow, Bishop of Exeter. He matriculated at Corpus Christi, Oxford on 2 August 1690, aged 16, and entered Middle Temple in 1691. In 1697 he was called to the bar. He married Mary Bidgood, daughter of Humphrey Bidgood of Rockbeare, near Exeter on 7 January 1695.
Drewe began his career as a barrister at Exeter. His father had political connections and influence and Drewe was returned unopposed as Member of Parliament for Exeter at the 1713 general election. His father died in 1714 and he succeeded to the Grange at Broadhembury.
Drewe was returned unopposed again at the 1715 general election, but faced a contest at the 1722 general election at which he was returned successfully. He was appointed a bencher in 1723. At the 1727 general election he was returned unopposed again and he retired in 1734. In Parliament, he voted consistently against the Government.
Drewe died aged 60 on 13 September 1734. He and his wife had two sons and three daughters. His son Francis was High Sheriff of Devon in 1738.
- Foster, Joseph. "'Disbrowe-Dyve', in Alumni Oxonienses 1500-1714, ed. Joseph Foster (Oxford, 1891), pp. 406-439". British History Online. Retrieved 15 October 2018.
- "DREWE, Francis (c.1674-1734), of Exeter, and the Grange, Broadhembury, Devon". History of Parliament Online (1690-1715). Retrieved 15 October 2018.
- "DREWE, Francis (?1674-1734), of the Grange, Broadhembury, Devon". History of Parliament Online (1715-1754). Retrieved 15 October 2018.
|Parliament of Great Britain|
Sir Coplestone Bampfylde
| Member of Parliament for Exeter
With: John Rolle 1713-1715
John Bampfylde 1715-1722
John Rolle 1722-1727
Samuel Molyneux 1727-1728
John Belfield 1728-1734