The YouGov poll was taken in the wake of revelations in the Panama Papers that Cameron's late father had an offshore fund but before the prime minister admitted to having held shares himself in the company.
The new survey showed Cameron's approval rating at 34 per cent compared to 39 per cent in a similar poll in February. The same rating for opposition Labour leader Jeremy Corbyn rose to 30 per cent compared to 25 per cent.
The poll also showed Cameron and finance minister George Osborne to be the least trusted politicians on tax avoidance, with 68 per cent of respondents saying they would not trust the British prime minister.
Seventy per cent said they would not trust Osborne. Cameron admitted yesterday he had held a 30,000 pounds stake in the offshore fund, selling the stake in the Bahamas-based trust in 2010, four months before he became prime minister.
Downing Street issued four statements following Sunday's publication of the leaked files, which showed how Panama-based law firm Mossack Fonseca had helped firms and wealthy individuals set up offshore companies.
He initially dismissed the story as a private matter before saying he and his wife and children would not benefit from any offshore funds in the future. The prime minister maintains that he paid full income tax on the dividends paid by the fund.
Labour MP John Mann said Cameron had "no choice but to resign", and is to call for an investigation into whether Cameron broke the MP's code of conduct. Cameron's popularity had already slipped as a result of the widening divisions in his Conservative party over the EU referendum.
He is leading the campaign for Britain to stay in the European Union in the June 23 referendum. But London's Tory mayor Boris Johnson, six senior Conservative ministers and an estimated third of the party's 330 MPs are backing a so-called Brexit.