He studied for a time at St. John's College, Cambridge, but did not graduate, and was afterwards called to the bar from Lincoln's Inn.

In May 1791, he married Harriott Lucke of Sussex, widow of Thomas Douglas, by whom he had two daughters.

Jermyn amassed materials for a history of Suffolk in conjunction with his friend David Elisha Davy [q. v.], each receiving a copy of the other's work.

At Davy's request Jermyn's collections were not sold at the sale of his effects in 1821, but were subsequently bought by Herbert Gurney, and presented to the British Museum in 1830.

James Jermyn [q. v.], cousin of Henry Jermyn, accused Davy, in a published pamphlet, of fraud in his relations with his cousin, but Davy vindicated his conduct in notes to the copy which is now at the British Museum.