Although Anstey declared himself uninterested in public office, he had served as High Sheriff of Cambridgeshire and Huntingdonshire for 1770–71, on the eve of his move to Bath. Once there, he busied himself in various philanthropic ventures, such as supporting the scheme for the support of the poor on behalf of which the Batheaston Circle's "Poetical Amusements" were sold. In addition he served between 1781 and 1795 on the board of governors of Bath Hospital, for whom he wrote effective fund-raising poems. Later he supported the work of Hannah More, in whose series of Cheap Repository Tracts appeared his long ballad, "The Farmer's Daughter, a poetical tale" (1795). His final Latin poem, the Alcaic stanzas addressed to Edward Jenner on his work on inoculation (1803), demonstrated the persistence of his humanitarian interests.