At sixteen he left Dedham school to study anatomy and surgery under Philip Meadows Martineau of Norwich, and removed in 1800 to the university of Edinburgh.
in the latter year, for which occasion he wrote a thesis entitled ‘De Animalibus in hyeme sopitis.’ Removing to London to continue his studies, he frequented the house of Anna Laetitia Barbauld and Dr. John Aikin, formed a friendship with Sir Humphry Davy, met Sir Joseph Banks, Isaac D'Israeli, and Samuel Taylor Coleridge.
In 1805 he started on a foreign tour, spent some months at Neuchâtel, traversed Switzerland, and ventured, with an American passport, on French territory at Geneva.
Reaching Vienna on 30 September, he was there an eye-witness of the scenes that followed Austerlitz (5 December), saw Napoleon at Schönbrunn, heard Girolamo Crescentini sing, had an interview with Joseph Haydn, and was present when Beethoven, ‘a small, dark, young-looking man,’ directed a performance of ‘Fidelio.’ At Berlin, moreover, in the spring of 1806, he became acquainted with Martin Heinrich Klaproth and Alexander von Humboldt, and was among the auditors of Johann Gottlieb Fichte.
He married, in 1807, Susan, eldest daughter of John Taylor of Norwich, one of that family by whom, according to the Duke of Sussex, the saying was invented that ‘it takes nine tailors to make a man.’ Mrs. Reeve was a sister of Sarah Austin, and died in 1864, having survived her husband fifty years.