As a young man Wooddeson frequented Thomas Payne's house and literary circle at Mews Gate.
He died, unmarried, on 29 October 1822 at his house in Boswell Court, Lincoln's Inn Fields, and was buried on 5 November in the benchers' vault in the Temple church.
The first, which appeared in 1783, was Elements of Jurisprudence treated of in the preliminary Part of a Course of Lectures on the Laws of England (London; new edit.
Originally delivered as a series of Vinerian lectures commencing in Michaelmas term 1777, and extending over a course of years, the latter work was a contribution towards systematising English law.
Wooddeson was the author also of A Brief Vindication of the Rights of the British Legislature, in Answer to some Positions advanced in a Pamphlet entitled "Thoughts on the English Government, Letter the Second", a reply to John Reeves, London, 1799.
He also made research collections for a work on tithes; but in poor health he asked Samuel Toller to carry out the plan.