LONDON—U.K. Prime Minister David Cameron on Sunday took the unusual step of releasing some of his income tax information in an effort to answer persistent questions about his financial affairs, after admitting earlier that his handling of the disclosure of links to offshore funds could have been better.

Even though Mr. Cameron claims he is the first U.K. prime minister to publish his income tax information, he may face further questions after his office confirmed he had received two gifts of £100,000 each, about $160,000 each...