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MPs have backed calls for a statutory register of commercial lobbyists who have access to Parliament.

It comes after undercover reporters from public affairs company Bell Pottinger boasting of their power to influence David Cameron.

Labour MP John Cryer introduced a Ten Minute Rule Bill demanding change.

His party says ministers are "too close to corporate interests", but No 10 said no lobbying firm "has any say or influence over government policy".

The government has said it plans to launch a consultation on statutory regulation of lobbying "shortly", with legislation introduced next year, in the second session of Parliament.

Introducing his bill in the Commons, Mr Cryer said there was "a very strong mood amongst the public to make lobbying more transparent and accountable".

"This bill would not impede the ordinary lobbyist - in other words, the ordinary constituent or member of the public who has a right to lobby his or her Member of Parliament," he said.

Instead, he said it would help level the playing field for smaller local interests, such as residents and tenants groups, who were being squeezed out by corporations with greater "financial muscle".

Conservative MP Philip Davies opposed the bill, accusing Mr Cryer of wanting to outlaw lobbying by businesses altogether - while maintaining the right of trade unions to do it.

"I would say that lobbying plays a very important part in any democratic process," he said. "It gives a voice to a whole range of groups... by allowing them to make their case."

Reporters from the Bureau of Investigative Journalism secretly recorded Tim Collins, managing director of Bell Pottinger Public Affairs, claiming to have access to the prime minister and the Chancellor, George Osborne.

Mr Collins, a former MP and director of communications for the Conservatives, also said he was close to Mr Cameron's policy adviser Steve Hilton and Downing Street chief of staff Ed Llewellyn.

The Independent newspaper, which published the recordings, quoted him as saying: "I've been working with people like Steve Hilton, David Cameron, George Osborne for 20 years-plus.

"There is not a problem getting the messages through."

Mr Collins, a former Tory MP who lost his seat in 2005, told the reporters he had worked with Mr Cameron and Mr Osborne in the Conservative Party's research department, and that Mr Llewellyn had worked under him at Conservative Central Office.

He also reportedly claimed that Bell Pottinger had recently persuaded the prime minister to raise the matter of copyright infringement with Chinese premier Wen Jiabao on behalf of engineering firm Dyson.

"He was doing it because we asked him to do it," he said.

The prime minister's official spokesman said the reported claims "totally misrepresent the relationship with Downing Street" and were a "gross exaggeration".

"It simply isn't true that Bell Pottinger or any other lobbying company has influenced government policies," he said.

The spokesman said it was in the interest of such companies to tell their clients they could provide high-level access.

And on the subject of the PM's meeting with Wen Jiabao, he added: "It is unsurprising that in a conversation with the Chinese, we might talk to them about intellectual property rights."

Deputy Prime Minister Nick Clegg said the events demonstrated the need for the government to press ahead with plans for a statutory register of lobbyists "so they have to show what they're doing and who's paying them and who they're trying to influence".

"There's nothing wrong with lobbying in theory, as long as it's done transparently in practice, and that is what we'll be seeking to do and pass through legislation as soon as we can," he added.

But Labour is calling for the government to make an urgent Commons statement on the issue of lobbying.

The ´óÏó´«Ã½ News Channel's chief political correspondent Norman Smith said they were also expected to write to Cabinet Secretary Sir Gus O'Donnell to ask him to investigate.

Shadow Cabinet Office minister Jon Trickett said the investigation had raised "very serious allegations".

"We have been calling on the government to implement a statutory register of lobbyists," he said.

"We need reform to ensure that there is no question of the rich and powerful buying access to the prime minister and his advisers."

Conservative MP Jesse Norman said that while there was "a serious problem" with some types of lobbying, it was important to distinguish between that and "proper communication".

"Proper communication is actually expressed in this story," he told ´óÏó´«Ã½ Radio 4's World at One.

"There was a case in which Dyson had found itself having its products ripped off by Chinese manufacturers [and] contacted Bell Pottinger. They were then able to make the case directly to Number 10 and that was taken up with the Chinese premier.

"It's representing a clear public interest, which is that British manufacturers should be able to play on level terms with Chinese manufacturers."

Lord Bell, chairman of Bell Pottinger's parent company Chime Communications, told the Press Association the firm would be making a formal complaint to the Press Complaints Commission on the grounds that there was "no public interest in this story".

In a statement through his lawyers, Lord Bell told the Independent: "The conduct of the Bureau of Investigative Journalism does not remotely constitute responsible journalism.

"It is an attempt by unethical, underhand deception to manufacture a story where none exists."

The issue of lobbying came to the fore recently with concerns about access to former defence secretary Liam Fox via his friend Adam Werritty.