He was the son of Sir Roger Jenyns and his second wife Elizabeth Soame, daughter Sir Peter Soame. He was born in London, and was educated at St Johns College, Cambridge. In 1742 he was chosen M.P. for Cambridgeshire, in which his property lay, and he afterwards sat for the borough of Dunwich and the town of Cambridge. From 1755 to 1780 he was one of the commissioners of the board of trade.

For the measure of literary repute which he enjoyed during his life Jenyns was indebted as much to his wealth and social standing as to his accomplishments and talents, though both were considerable. His poetical works, the Art of Dancing (1727) and Miscellanies (1770), contain many passages graceful and lively though occasionally verging on licence.

The first of his prose works was his Free Inquiry into the Nature and Origin of Evil (1756). This essay was severely criticized on its appearance, especially by Samuel Johnson in the Literary Magazine. Johnson condemned the book as a slight and shallow attempt to solve one of the most difficult of moral problems. Jenyns, a gentle and amiable man in the main, was extremely irritated by his review. He put forth a second edition of his work, prefaced by a vindication, and tried to take vengeance on Johnson after his death by a sarcastic epitaph:

Here lies poor Johnson. Reader, have a care,

Tread lightly, lest you rouse a sleeping bear;

Religious, moral, generous, and humane

He was...but self-sufficient, rude, and vain;

Ill-bred and over-bearing in dispute,

A scholar and a Christian...yet a brute.

In 1776 Jenyns published his View of the Internal Evidence of the Christian Religion. Though at one period of his life he had affected a kind of deistic scepticism, he had now returned to orthodoxy, and there seems no reason to doubt his sincerity, questioned at the time, in defending Christianity on the ground of its total agreement with the principles of human reason. The work was deservedly praised for its literary merits.

His heir was his cousin George Leonard Jenyns.

A collected edition of the works of Jenyns appeared in 1790, with a biography by Charles Nalson Cole. There are several references to him in James Boswell's Johnson.