David Cameron and his family will not benefit in the future from any offshore funds, his spokesman has belatedly revealed, following repeated failures to provide a full account of the prime minister’s links to a controversial overseas company set up by his late father.

Cameron has come under increasing pressure to give a clear explanation of how and whether he, his wife and children stood to benefit from Blairmore, the Bahamas-based company set up by his father Ian, which avoided ever paying tax in Britain.

The prime minister and his office gave three partial answers about the fund on Tuesday but crucially failed to say whether Cameron and his family would gain in the future from Blairmore, an investment fund.

But on Wednesday his spokesman provided further clarity. “There are no offshore funds/trusts which the prime minister, Mrs Cameron or their children will benefit from in future,” he said.

A statement on Tuesday only said the Camerons are not currently benefiting from the offshore fund.