The President of the Board of Trade met a group of more than 20 Labour MPs before last night's vote to persuade them that the Bill and European case law was sufficient to deal with predatory pricing by Mr Murdoch's News International group, owners of the Times; and Tony Blair held private meetings with some backbench critics to reinforce her assurances.
But fears were not allayed when Mrs Beckett announced she would be seeking to throw out from the Bill an amendment made in the Lords by Lord McNally, the Liberal Democrat peer, with the support of Labour peers, to outlaw the abuse of a dominant position by a national newspaper.
Mrs Beckett was effectively served notice by senior Labour backbench MPs that there could be a rebellion during the Bill's later stages in the Commons, unless it is strengthened.
Chris Mullin, the Labour chairman of the Commons Home Affairs select committee, said: "We aren't talking about interfering in the free market. We are talking about subverting of the free market." He said predatory pricing had taken pounds 100 million in profit out of the broadsheet market.
Calling for a separate media Bill, Clive Soley, the chairman of the Parliamentary Labour Party, said: ``I have no doubt we need a mechanism for taking tougher action when there is predatory pricing."
David Winnick, a veteran Labour MP, said: "What is really required is effective legislation. The situation whereby the Times is deliberately undercutting other newspapers to drive them out of business is totally undesirable."
The argument centres on Mrs Beckett's assurances that a European court judgement, known as the Tetra Pak case, established that predatory pricing would be illegal. Mrs Beckett said that the European Court of Justice ruled in that case that if prices were shown to be below the average variable cost of production, predatory pricing should be assumed.
"Even if prices are above average variable costs but still below total average costs, conduct is to be regarded as predatory if it can be established that the purpose of that conduct is to eliminate a competitor," she told MPs. A leading Labour pro-European, Giles Radice, Labour chairman of the Commons Treasury committee, said the law set out in that case "was quite tough" and would catch News International. "We should look carefully at Mrs Beckett's statement. I intend to get legal advice on it... I want to consider what happens in committee and I want to decide then what happens at the report stage."
But David Chidgey, the Liberal Democrat spokesman, said he had received legal advice that the Tetra Pak case could only apply to newspapers which had already established a dominant position - 40 per cent of the market or as low as 20 per cent depending on the nature of the market.
He said it would not apply to newspapers, such as the Times, which he said had a six per cent share, before they reached a dominant position.