Member of Parliament and member of the House of Keys, and the Duke of Atholl's most effective opponent in the Commons.

He came of the Milntown Christian family, and one Manx commentator records him as the only person ever to have sat at the same time in the British Parliament and in the House of Keys. He was no friend of the Duke, and he was a considerable mover in the improvement of Manx agriculture. David Robertson dedicated his Tour through the Isle of Man of 1794 to him.

His set-piece was the debate of 7 June 1805. The Duke of Atholl had petitioned for further compensation for the rights sold in 1765, and a committee of the House of Commons reported that he had fully established his allegations and that compensation should be granted, charged on the revenue of the Island. When that report came before the House, Curwen spoke against it, and the House of Keys afterwards voted him their thanks. The opposition carried its real point. The Duke did obtain an additional revenue, but it was made a charge on the Consolidated Fund and not on the Manx revenue. His speech was printed the same year.

He spoke to the state of the Island as well as its politics. In 1805 he put the productive acreage at a hundred and sixty thousand, at an average rental of ten shillings, and told the Commons that no inconsiderable proportion of the duties arising in the Isle of Man were on goods paying low duties which were afterwards clandestinely re-shipped and smuggled back into England.