He was nominated by his father as a fellow of Christ's on the Finch and Baines foundation in 1713 and was awarded MA in 1714.
[2] Finch stood unsuccessfully for Parliament as a Whig in the Cambridge University by-election on 19 December 1720.
By 1724 he had been over ten years at Cambridge and his father and his brother Lord Finch were in discussion over his future.
He was returned as Member of Parliament for Malton at a by-election on 27 November 1724 on the interest of his brother-in-law, Thomas Watson Wentworth.
In 1743 he left the Minorca post and was appointed surveyor of works on the recommendation of Pelham in preference to his brother Edward.