Atkinson was the son of the rector of Thorpe Arch, York, of the same name, one of his twelve children, of which at least two also became clergymen. He was educated at Trinity College, Cambridge where he became a Fellow and Tutor. In 1785 he married Catherine, the sister of Sir John Fleming Leicester, 1st Lord de Tabley (1762-1827), who built up a famous collection of British art. Atkinson was one of the first Methodists and rector of Wethersfield in Essex. He was a fine ornithological artist and his grandson the Rev. John Atkinson (1814-1900) wrote a popular book on birds’ nests and eggs.