The Prime Minister said he was determined to ensure 'high standards of probity right across government', but rejected Mr Blair's call for the Committee of Privileges inquiry into allegations of payments for tabling Commons questions to be held in public.
Mr Major had come prepared with what amounted to a short statement on claims that Mr Hamilton and Mr Smith, before becoming ministers, were paid through an independent lobbying firm to act on behalf of Mohamed Al Fayed in his fight with Lonrho to keep control of Harrods.
He delivered it in response to Michael Clapham, Labour MP for Barnsley West and Penistone, who asked when Mr Major had become aware of the allegations.
The Prime Minister said: 'The allegations were brought to me privately some three weeks ago. It was clear that the allegations . . . originated, but did not come to me directly, from Mr Al Fayed. I made it absolutely clear at that time that I was not prepared to come to any arrangement with Mr Al Fayed.' Backbenchers jeered and roared their astonishment.
'I made it perfectly clear that these matters would be fully investigated and I immediately asked the Cabinet Secretary (Sir Robin Butler) to undertake an independent and full investigation.
'Mr Smith has written to me following that investigation and discussions with the Cabinet Secretary to say he did have a business relationship with Mr Al Fayed and was paid a fee. He did not, however, declare the detail in the Register of Members' Interests during the consultancy. He has tendered his resignation and I have accepted (it).'
Mr Major continued: 'Mr Hamilton has written to me explicitly refuting the allegations that he was paid any money, either to ask questions or to undertake any activity whatsoever on behalf of Mr Al Fayed. He has announced he will be instituting legal proceedings for libel.'
Mr Blair put three proposals to the Prime Minister. First, that no minister who had privatised a company should subsequently end up on its board.
Second, Mr Major should publish a list of all members of quangos, their payments, perks and any position with any political party.
'Third, that the cash-for-questions inquiry now be broadened, be made deeper, be held in public and be made fully independent - so that the confidence of the British people in their government can begin to be restored.'
Mr Major replied that he would not tolerate anything less than the highest standards of behaviour. But he said he was not prepared to act on the basis of unsubstantiated allegations and when the persons concerned had given 'concrete assurances' that the charges were without foundation.
On quangos, he said an independent working body to look at the system of appointments was set up last May and he expected its report shortly. The Treasury and Office of Public Service had been preparing revised guidance on making appointments and David Hunt, Chancellor of the Duchy of Lancaster, had been asked to look at appointments to public bodies and make recommendations on changes, if necessary. He said there was no precedent for the Committee of Privileges not sitting in private. Its report would be published and debated on the floor of the Commons. As for seats on privatised company boards, Mr Major said he knew of 'no occasions where the question of abuse of previous ministerial interest arises'.
Paddy Ashdown asked if the Prime Minister realised just how disappointed many people would be with his 'inadequate' answers to Mr Blair's proposals.
'Neither this House nor the people of this country are going to be satisfied with the result of inquiries held in secret,' he said.