LONDON—The resignation of a U.K. government minister citing differences over economic policy has exposed fresh divisions within Prime Minister David Cameron’s ruling Conservative Party already split over membership of the European Union.

Iain Duncan Smith, one of a handful of ministers who broke ranks with the prime minister to campaign for so-called Brexit ahead of June’s national EU referendum, announced in a letter late on Friday that he was stepping down as work and pensions minister because he believed the government’s...