The whole issue has been dismissed by the prime minister as "froth".
In a speech to the Tory Carlton Club on Tuesday evening Mr Hague said revelations in former paymaster general Geoffrey Robinson's book had confirmed that "this Labour government is a rotten government".
He said: "Now only the prime minister can act to restore confidence in the integrity of government - he must do so urgently."
Mr Hague's speech was widely seen as an attempt to maintain pressure on the government in the light of allegations in Mr Robinson's book, being serialised in the Daily Mail this week.
Mr Robinson was forced to resign from the government in 1998 after it emerged that he gave a secret £373,000 loan to the then Trade Secretary Peter Mandelson.
Mr Mandelson - who resigned at the same time but has since been given a new job as Northern Ireland secretary - had claimed that Mr Robinson had offered the loan.
In his book, millionaire businessman Mr Robinson said Mr Mandelson had requested the loan.
The whole issue has been dismissed by the prime minister as "froth".
Mr Blair said: "Whatever the froth of the day to day, the only thing that matters to people are the fundamentals."
And his official spokesman insisted that nothing was new in Mr Robinson's book.
But after Mr Hague's speech, Tory trade spokesman David Heathcoat-Amory said Mr Robinson's memoirs highlighted the case for an inquiry into Labour party funding.
That was taken to refer to other accusations that Mr Robinson bankrolled Mr Blair's office in the run-up to the 1997 election.
Mr Heathcoat-Amory said: "I am intrigued by one passage from his book where Geoffrey Robinson says that he has made 'many such gestures: some bigger, some smaller, some as gifts and some as loans'.
"So who received bigger loans than Mandelson?" he said.