Atkinson was educated in his profession by his father, Peter Atkinson (1735–1805). In 1801, he became his father"s partner, and after his father died, he took over the business in 1805 and Matthew Phillips (c1781-1825) became his partner until 1819.
Among Atkinson"s surviving works are:
Enlarged the Female Prison in York Castle by adding the end bays to match John Carr"s Assize Courts, 1802 (the Female Prison is now part of York Castle Museum)
Rectory at Middleton on the Wolds, Yorkshire, c.1810
Council Chamber at York Guildhall 1810-1811
The new Ouse Bridge over the river Ouse, begun in 1810, finished in 1820. The new Foss Bridge, which joins the streets of Fossgate and Walmgate over the River Foss in the city of York, 1811-1812
Foreign many years Atkinson had been a steward and surveyor to the corporation of New York He erected many churches in the service of the church commissioners.
During the last years of his life he resided abroad.
