"I don't believe that Mr Willetts acted as a sole operator and made mistakes. This man is at the very heart of the government operation," said Mr Prescott.
Andrew Mitchell, a former whip, is expected to be the first to be questioned under oath under the new code of conduct by the committee on standards and privileges in the wake of the Willetts report.
"I cannot believe for a moment throughout this period of time there haven't been close discussions," Mr Prescott said. "Mr Mitchell was a whip appointed to this committee ... whose job solely was to try and cover up for the Government. That is at the heart of this question, more than Mr Willetts. He has resigned but there are other guilty people involved in this operation. It involved government right at the core of its operation."
Mr Mitchell, now a social security minister, tipped off the Chief Whip in a note that he had spoken to the clerk of the predecessor committee investigating the cash-for-questions allegations against another minister, Neil Hamilton.
As a member of the committee, he had a right to speak to the clerk. But ministers said an apology was likely to be made to avoid any embarrassment for the Government. "The lesson we have learnt from the Willetts affair is to apologise," said a minister.
The Standards and Privileges Committee next week will question Sir Gordon Downey, the parliamentary ombudsman, on his investigation into the Hamilton affair.
The Government moved quickly to limit the damage with a mini-shuffle to fill the gaps caused by Mr Willetts' resignation - Michael Bates was promoted from the whips' office to Paymaster General; Giles Brandreth was promoted to replace Mr Bates; and Matthew Carrington, MP for Fulham, was appointed as a whip.
Mr Willetts also rejected calls by Mr Prescott for him to step down from politics. He said he would be continuing as the MP for Havant, and ministers, led by Stephen Dorrell, the Health Secretary, rallied round to say he would be back as a frontbencher after the election.
There were fears among the Labour leadership that the ferocity of Mr Prescott's attack could lead to a Tory backlash on the committee. Leadership sources were keen to refocus their attack on Mr Hamilton. A senior source said: "Willetts is a dead body on the battlefield. He is a distraction and so is Mitchell. We should be focusing on the main issue, which is corruption at the heart of the Government."