[2][4] In 1760, his father approached Thomas Braidwood, owner of a school of mathematics in Edinburgh, seeking an education for the boy, then ten years old, in the hope that he could be taught to write.

[2] Shirreff successfully exhibited oil paintings, pastels, and pencil drawings at the Royal Academy of Arts in 1771, and at the Free Society of Artists from 1770 until 1773.

[3] He befriended Caleb Whitefoord, a well-connected Scottish merchant, diplomat, and political satirist who moved in London's wealthiest elite circles, where Shirreff developed advantageous associations with portraitists Sir Joshua Reynolds, George Dance the younger, and Richard Cosway.

[6][8] During that period, he had clients for portraits in common with two other deaf miniaturists in Bath, Sampson Towgood Roch and Richard Crosse.

[4] More recent biographies give an earlier year of death,[9] based on probate records showing that Shirreff must have died prior to 5 November 1829, when his will was proved in court.

[2] On 11 January 1810, Shirreff married Mary Ann Brown, the sister of a fellow artist, at St George's, Hanover Square.