Barrington served as a Vice President of the Royal Society and wrote on a range of topics related to the natural sciences including early ideas and scientific experimentation on the learning of songs by young birds.

[citation needed] He subsequently held various legal offices, including marshal of the High Court of Admiralty, 1751–3; a judge of Great Sessions for North Wales (Anglesey, Caernarfonshire and Merionethshire) from 1757; Recorder of Bristol and King's Counsel from 1764; and second justice of Chester from 1778.

Though considered by some (including Jeremy Bentham) to be an indifferent judge, his Observations on the Statutes, chiefly the more ancient, from Magna Charta to 21st James I (1766), had a high reputation among historians and constitutional antiquaries,[2] and ran through five editions down to 1796.

His Tracts on the Probability of reaching the North Pole (1775) were written in consequence of the northern voyage of discovery undertaken by Captain Constantine John Phipps, afterwards Lord Mulgrave (1744–1792).

…I must add [the fact that] I have been informed by two or three able musicians, when Bach the celebrated composer[note 1] had begun a fugue and left off abruptly, that little Mozart hath taken it up, and worked it after a most masterly manner.

[2] Barrington attempted cross-fostering experiments on birds and noted that young linnets raised with foster parents could be induced to learn the songs of various lark species.

Barrington established the format of the Naturalist's Journal for "keeping a daily register of observations on the weather, plants, birds, insects, &c" based on Benjamin Stillingfleet for collating information from across England.