The move follows concern about the attempt by Rupert Murdoch's BSkyB to take over Manchester United Football Club in a pounds 623m deal.
Lord Borrie, a former director-general of the Office of Fair Trading, last night urged the Government to set up an independent inquiry to examine the law on media ownership.
Lord McNally, a Liberal Democrat peer, is also writing to Peter Mandelson, the Trade and Industry Secretary, making the case for a Royal Commission to reassess the potential for conflicts of interest.
The proposal will be formally put to Parliament when the Competition Bill returns to the Lords next month. Lord McNally plans to table a wide- ranging amendment to the proposed legislation that will give peers the opportunity to debate the issue.
Government ministers are considering establishing an independent watchdog to oversee football. The department of Culture, Media and Sport last week discussed setting up a new body to calm worries about the future of the sport. They believe that the OFT and the Monopolies and Mergers Commission may not be specialised enough to deal with the specific issues surrounding football.
Meanwhile, it has emerged that City financial advisers Salomon Smith Barney, the US-based investment bank, and HSBC Holdings, met last Monday to discuss a rival bid for Manchester United, on behalf of a mystery bidder, to trump Mr Murdoch's offer.
Mr Mandelson has referred the BSkyB bid to the OFT, which will decide if the Monopolies and Mergers Commission should investigate the matter.
However, Lord Borrie said the existing rules on media ownership were inadequate. He stressed that the Manchester United bid was not necessarily anti-competitive itself but said it highlighted a wider problem.
He called for a Royal Commission to be set up to assess whether or not it was appropriate for newspaper proprietors to own other businesses.
"There is such a danger that individual proprietors who have a variety of business interests allow those other concerns to get in the way of editorial freedom and independence," he said.
"Once they own a newspaper there is a strong temptation to ensure that the newspaper editors go along with the proprietor's interests. A Royal Commission could examine the whole issue."
Lord McNally, who earlier this year led the campaign to impose tighter controls on the operation of Mr Murdoch's newspaper empire, said the law had failed to keep up with fundamental changes in the way the media was run.
"I don't think the political process and the regulatory process have caught up with the technology. What we have got now is a concentration of power in the hands of a few people," he said.
"There is a need for a proper overview of where we are and what we need to do to ensure fair competition and to make sure that there are proper constraints on the power that people like Mr Murdoch have."
Earlier this year, peers voted to impose additional restraints on newspaper proprietors, and many expressed particular concern about the decision by Mr Murdoch to cut the price of the Times to 10p.
The Government used its huge Commons majority to overturn their amendment to the Competition Bill. But the issue will be fiercely debated when the proposed legislation returns to the Lords.
Labour's All-Stars, page 23
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