A Labour MP has alleged that phone hacking at News International has gone "far beyond the News of the World" as he claimed that the Sun newspaper is also implicated in illegal practices.

Tom Watson made the allegation during an emergency motion debate on the phone-hacking scandal at the Labour party conference which called for James Murdoch to stand down as chairman of BSkyB in the wake of the phone hacking scandal that rocked Rupert Murdoch's media empire this summer.

The scandal took centre stage at the party conference on Tuesday morning as speakers took turn to lament Labour's past era of cosy relationships with media barons and called for measures to clamp down on bad practice by media companies and journalists.

Watson warned Labour activists that the scale of phone hacking at the now closed News of the World could be the tip of the iceberg.

"Do you really think that hacking only happened on the News of the World?" he said. "Ask Dominic Mohan, the current editor of the Sun. He used to joke about lax security at Vodafone when he attended celebrity parties. Ask the editor of the Sun if he thinks Rupert Murdoch's contagion has spread to other newspapers. If he gives you an honest answer, he'll tell you it's only a matter of time before we find the Sun in the evidence file of the convicted private investigator that hacked Milly Dowler's phone.

"This month we learn that journalists at the Times are affected by this scandal. The paper is shutting down its BlackBerry phone network – I hope they aren't deleting the records."

The emergency motion called for trade unions to have a role on the press watchdog and for the rules governing media ownership in Britain to be examined in the wake of the affair.

Watson turned on the case for applying the "fit and proper" test to News International, a company he described as "sick" with corruption and criminality from "top to bottom".

"Let's tell Ofcom what we think about James Murdoch," he said. "I wouldn't put him on the board of an ornamental garden. He's certainly not a fit and proper person to chair a major broadcaster."

Watson was among a number of speakers who hailed the leadership of Ed Miliband following revelations over the summer of how widespread phone hacking had been at News international, and contrasted it to Labour's past closeness to Rupert Murdoch under Tony Blair and Gordon Brown.

Watson, who received a standing ovation from delegates over his persistent questioning on phone hacking, said MPs had to "accept our shame of the blame" but that Labour had acted quickly in response to hacking allegations.

He said that hacking had been allowed to take place because of "police failure, a newspaper out of control, politicians refusing to act".

"There is no point in us glossing over it. We got too close to the Murdochs and allowed them to become too powerful," he said. "As a party, we got there in the end. When Ed [Miliband] got up at prime minister's question time and said what he said about the Murdochs, like you I thought, 'That is the leader I want'. This is the Labour party I want to be part of."

He went on: "Now our leadership must spearhead seeing the reforms through. It is not just about the News of the World or just about phone hacking. Murdoch should also tell us about the computer hackers, the people who left Trojan devices on computer hard-drives enabling them to read emails."

Chris Bryant told the conference that Labour's past relationship with the Murdoch empire was "not our finest moment" as he urged the party to "choose our bedfellows with a little more care" in the future.

Ivan Lewis, the shadow culture secretary, underlined Labour's new approach to the media mogul as he told delegates that Labour would create "tougher" media ownership laws and a register which could see errant journalists barred from the profession.

In a message to Rupert Murdoch, he said: "Mr Murdoch: never again think you can assert political power in pursuit of your commercial interests or ideological beliefs. This is Britain, Mr Murdoch, the integrity of our media and our politics is not for sale."

Lewis said the history of the relationship between Labour and the Murdoch press was a "complex and tortuous one".

"But what can never be complex or tortuous is the responsibility of politicians to stand up in the public interest without fear or favour."

Setting out his reforms, he said: "Never again can one commercial organisation have so much power and control over our media. In the period ahead, Labour will bring forward proposals for new, tougher cross-media ownership laws."

While a free press was "non-negotiable", Lewis said that with freedom also comes responsibility. "Neither the current broken system of regulation nor state oversight will achieve the right balance," he said.

"We need a new system of independent regulation, including proper, like-for-like, redress which means that mistakes and falsehoods on the front page receive apologies and retraction on the front page. And as with other professions, the industry should consider whether people guilty of gross malpractice should be struck off."

Lewis also said it was time David Cameron "came clean" about the appointment of former NoW editor Andy Coulson as his communications chief.

Bryant, a former minister whose phone was hacked, told Labour delegates that he hoped those involved in phone hacking and the ensuing cover-up would go to jail.

He hit out at those who had "lied and lied and lied" to parliament during the hacking investigation. Earlier this month, he claimed that he had tracked 53 lies told to parliament. But he said his tireless researcher had now tallied that a total of 486 lies had been told to parliament.

"I hope that people will go to jail for the criminal cover-up that happened at News of the World," he said. "But there is a bigger scandal, because it is the monopoly that BSkyB have. The fact that they've got 80% of the pay-TV market and 95% in the pay-TV market in many places. They can hoover up television rights, and hardly produce a decent programme of their own. That is one of the things that we should be dealing with – the monopoly at BSkyB.

Unite general secretary Len McCluskey pressed for a "long overdue" review of the rules governing media ownership in the UK and told the conference that there should be an element of "shame" in the party over the way past leaderships helped to "prop up" the Murdoch empire.

In a swipe at former premier Tony Blair, he said: "The Labour party needs to learn lessons – and they won't be learned by standing down by the banks of the Jordan blessing Murdoch's children."

"They will be learned by setting up the two commissions called for in this motion. One is for an overdue look at the rules controlling media ownership and the unacceptable concentration of power, of which the Murdoch empire is the worst example. And the second is to look at a still wider question – how independent trade unions are essential in ensuring that the rich and powerful do not get it all their own way. That they do not control our politics without the slightest counter-balance in society as a whole."

Miliband has pledged to work with Hollywood star Hugh Grant on media reforms.

The actor, who has become a champion for the Hacked Off campaign that is pressing for tougher sanctions and restrictions on the press, claims some newspapers will be "back to their old tricks" soon and questioned whether Labour MPs would still stand up to the media when the furore had died down.

Grant met the Labour leader on Monday night to press his case at the party's conference in Liverpool.

A senior Labour source said it was an "excellent meeting".

"Ed expressed his thanks for Hugh's work in the Hacked Off campaign and they said they would work together in future."

News International has hit back at Watson's allegations that staff on the Sun were implicated in illegal phone hacking and said if he had any evidence to suggest this was the case he should immediately hand it over to the police.

In a statement it said: "Everyone should act responsibly regarding the current investigations to allow the police to get on with their important work.

"If Mr Watson has specific information he should immediately hand it to the police and we urge him to do so. We are not aware of any evidence that the Sun engaged in activity as suggested by Mr Watson."