Mr Norman, MP for Tunbridge Wells, said it was galling to see businessmen lining up to back Tony Blair when the threat to enterprise today came from a new form of "regulatory socialism" practised by his Government.
Speaking at the Confederation of British Industry conference in Birmingham, Mr Norman admitted this was partly the fault of his party. "I fully accept that the Conservatives in the dying days of the last government lost touch. We lost touch with our own people, business people, entrepreneurs, shopkeepers and the self-employed," he said.
He also admitted that the Conservatives themselves had failed to ease the burden of regulation on industry despite the pledge by the former deputy prime minister, Michael Heseltine, to light a "bonfire of red tape".
"We Conservatives failed to reverse the tide of regulation. That was a failure. But the difference with New Labour is that they are riding the tide," said the Asda chairman.
This is the first time a senior figure within the party has been so candid in public about the way the Conservatives lost touch with their bedrock support in the business community.
It also signifies an attempt by the Conservatives to rebuild bridges despite the gulf between the party and business over its opposition to British membership of the single European currency for the next 10 years.
In a direct appeal to CBI leaders, Mr Norman said that if business was to preserve the gains of the past 18 years, Britain needed an enterprise alliance modelled on the successful Countryside Alliance.
There was a cautious response to Mr Norman's appeal. Sir Clive Thompson, president of the CBI, denied that business had fallen in behind New Labour. "We are not the business wing of the Labour Party and we are not a substitute for Her Majesty's Opposition," he said. "We look forward to the Tory party taking over the latter role."
Mr Norman told a CBI breakfast seminar that Britain needed an enterprise alliance because it was facing an "instinctively regulatory government and an unquestioning enthusiasm for the continental European social model". Labour, he said, was "regulation trigger-happy" and this was costing business tens of millions of pounds in unwanted and unnecessary restrictions and bureaucracy.
He pilloried European directives making it illegal to sell small apples and feta cheese in Britain and regulating the size of avocados, melons and garlic, describing EU regulation as "death by a thousand cuts".
Mr Norman also attacked the political motivation behind the inquiry by the Office of Fair Trading into supermarket pricing in the UK.