Wrangham was one of the few people to have known both Wordsworth and Coleridge before they knew each other. Coleridge met him during his last term in Cambridge and visited him in Cobham, Christmas 1794; Wordsworth met Wrangham in 1795 in London. It was probably after hearing Wordsworth read Salisbury Plain that Wrangham suggested they collaborate on a version of Juvenal's eighth satire.

Wordsworth visited Wrangham's house in Cobham for a few days in late July 1795, shortly before his departure for Racedown (Reed i 166). The ostensible reason must have been their collaboration, but Wrangham, who was already a book-collector, would have taken the opportunity to show his new friend his library. The catalogue of the English books in his library that he compiled, annotated, and printed privately in 1826, runs to 645 pages. As he states in his introduction: ‘I went on accumulating them to the verification of the prophecy of a witty neighbour, who predicted that “they would creep over my walls like an erysipelas” … My hall, dining-room, ante-room, dressing rooms, bed-rooms, garret, closets etc. … all overflow’ (Wrangham iii-iv). Something of his tenacity as a collector is implied by a letter of March 1813 to Sarah Priestley, a bookseller in London, requesting that she either sell him her books at the trade rate or pay their carriage to Yorkshire (BL Add.MS 28,654).