He was the son of William Aston, gunsmith, of Deansgate, in Manchester. In 1803 he opened a stationer's shop at 84 Deansgate, where, on 1 Jan. 1805, he issued the prospectus of the Manchester Mail, published at sixpence, and professing 'no political creed.' From 1809 till 1825 he was publisher and editor of the Manchester Exchange Herald, a conservative journal. Afterwards he removed to Rochdale, where he started the Rochdale Recorder. He died at Chadderton Hall, 19 Oct. 1844, and was buried at Tonge, adjoining Middleton. Aston was the friend and executor of Thomas Barritt, the antiquary. For about thirty-four years he also enjoyed the closest intimacy with James Montgomery, the poet, and editor of the Sheffield Iris, who submitted to him most of his manuscripts for revision and criticism. He himself was a facile writer of verses, the majority of which appeared in his own paper. Of his dramatic pieces, Conscience, a comedy, was performed at the Theatre Royal, Manchester, in 1815, with moderate success; and he also wrote Retributive Justice, a tragedy, and A Family Story, a comedy.
His published works nearly all relate to Manchester. They include The Manchester Guide, 1804, 2nd edition, 1815, 3rd, with plates, 1826; History and Description of the Collegiate Church of Christ, Manchester; Lancashire Gazetteer, 1st edition 1808, 2nd, 1822; An Heroic Epistle from the Quadruple Obelisk in the Market Place to the New Exchange, 1809; A Descriptive Account of Manchester Exchange, 1810; Metrical Records of Manchester, in which its History is traced (currente calamo) from the days of the ancient Britons to the present time, 1822.