Acton was the nephew and pupil of Nathaniel Wright, a London carpenter and surveyor.
He entered the Royal Academy Schools in 1790, and studied there for at least four years, receiving the silver medal in 1794.
His exhibits included a drawing of the interior of St Botolph's church (1791), and designs for mansions, villas and baths.
[2] Among his bequests he left £500 to establish a charitable fund for the benefit of members of the Surveyors Club and their dependents.
In 1838, his widow Hannah Acton gave £1000 in his memory to the Royal Institution to found the Actonian Prize.