[1] He went to Pembroke College, Cambridge in 1775, becoming friends with the future Prime Minister, William Pitt the Younger, and graduated with an MA in 1780.

He soon became a Treasury minister from 1782, and was a member of the government of the Younger Pitt from 1783, being appointed King's Remembrancer in the Exchequer of pleas in 1785.

One year later, and five days after the birth of their only child, a daughter named Harriot Hester, Eliot's wife died as a result of complication from childbirth.

He was active in lobbying the cause of the Clapham Sect in parliament and acted as a mediator between Wilberforce and Pitt in their campaigns.

[3][4] In 1793, having resigned from the Treasury on health grounds, Eliot was appointed joint commissioner for Indian affairs.