Mr Norris was one of the "star turns" at a private meeting of junior ministers with the Prime Minister at Chequers on Monday.
John Major used the meeting to sound out opinion among ministers on how the Tories can beat Tony Blair's New Labour. Mr Norris was said by colleagues to have "put into words what we were all thinking", and was being tipped to become a vice-chairman of the party in the summer reshuffle.
Ann Widdecombe, the Minister of State at the Home Office, is also said to have made a strong impression at a similar meeting for middle-ranking ministers at Chequers last week.
Ministers are expecting the reshuffle in July to be limited to the lower ranks.
The Prime Minister is being pressed to drop Douglas Hogg, the Minister of Agriculture, Virginia Bottomley, Secretary of State for National Heritage, and the Lord Chancellor, Lord Mackay, whose divorce law reform Bill is threatened by Labour and Tory rebels. Mr Hogg was accused of failing to persuade European ministers to lift the ban on beef. It was alleged he had refused to go to one European meeting "because he said he didn't work on Saturdays".
Mr Major was expected to stand by Mr Hogg, although David Davis was seen as a powerful candidate to replace him. Mr Davis, the Foreign Office minister, was responsible for sounding out Cabinet ministers on the options for retaliatory action over the ban on beef exports.
The Prime Minister's announcement of non-cooperation until the ban is lifted was widely seen by Tory MPs as a watershed for the Conservative Party, which lifted their chances of winning the election. Mr Norris, a junior Transport minister, is the only minister in Mr Major's government to have survived in office in spite of allegations of affairs. He has announced his intention to stand down at the next election from his Epping Forest constituency.
He has a reputation for being frank. On the day of the leadership election last July Mr Norris said many MPs saw Mr Major as the "least worst option". He is seen as a hard-hitting minister who could sharpen up the presentation of the Government's record, and help to lead the attack on Labour.Reuse content