He undertook almost fifty commissions, broadly distributed in the north of England and the Scottish lowlands, London and the surrounding counties, with occasional excursions to Herefordshire, Staffordshire, and Ireland.
He was probably the son of a William Atkinson who worked during the 1760s as a builder at nearby Auckland Castle, the palace of the bishops of Durham.
The younger Atkinson began work as a carpenter and in the mid-1790s came to the attention of the prominent architect James Wyatt, then making alterations to the castle, who took him as a pupil.
Atkinson seems never to have executed entire classical buildings, but before 1825 he carried out several additions or alterations to country houses in this style.
Atkinson also worked on seven churches, including Durham Cathedral, and All Saints', Newton Heath (1814–16), the only one wholly rebuilt to his designs.