But Labour MP Ian Lucas insisted that Mr Hain could continue in his Cabinet job even if the police are called in.

Legislation passed by the Labour government allows for criminal prosecutions if rules on political funding are breached, but the Electoral Commission declined to say whether this could be the outcome of its inquiry into Mr Hain's donations.

"We are not commenting on whether it is an option or not an option," said a Commission spokeswoman. "All we are saying is we are doing our initial compliance checks and will put the information we receive into our registers. Should there be any compliance issues, we will follow them up."

Mr Lucas said in an interview: "It's always been a possibility that the police might be brought in, because these are very serious matters".

But he insisted it was "entirely tenable" for Mr Hain to remain Work and Pensions Secretary during any police inquiry.

He added: "Peter Hain has said he has made mistakes, he has apologised and gone to the Electoral Commission and gone through all the disclosures that were made... It was perfectly in order for him to take the money. What was wrong, and he has admitted this, is that he ought to have disclosed it at the time."

Mr Hain has promised to cooperate fully with inquiries by the Commission and the Parliamentary Standards Commissioner into his failure to disclose more than £103,000 in donations to his failed deputy leadership bid last year.

But Conservatives demanded immediate answers to a set of questions about the gifts and about the Progressive Policies Forum (PPF) think-tank through which they were channelled.

Meanwhile, Conservatives were forced to fend off allegations about donations of flights made to David Cameron during his campaign for the party leadership in 2005.