Birch was born in Warwickshire, the son of Anne, née Russell, and physician Thomas Birch. He spent his early childhood in Warwick and was apprenticed to a jeweller, Thomas Jeffreys, and to Sir Joshua Reynolds. He exhibited enamel portraits at the Royal Academy from 1781 to 1794. In 1785, he received a medal from the Royal Society of Arts. As an engraver he is best known by his 'Délices de la Grande Bretagne,' consisting of thirty-six plates of ancient buildings in Norwich and elsewhere, published in 1791.
Emily T. Cooperman & Lea Carson Sherk, William Birch: Picturing the American Scene (University of Pennsylvania Press, 2010). The first biography of William Birch, it contains an edited version of his autobiography.