The government tonight came under pressure to set up a judicial inquiry into the phone hacking scandal at the News of the World after the paper confirmed that it has suspended a journalist while it investigates new allegations of the unlawful interception of voicemail.

The prime minister's media adviser, Andy Coulson, has denied a report in the New York Times which claimed he freely discussed the use of unlawful news-gathering techniques when he was editing the paper and "actively encouraged" a named reporter to engage in illegal interception of voicemail messages. Coulson has always denied knowing of any illegal activity by his journalists.

Scotland Yard, too, found itself in the firing line after the New York Times quoted unnamed detectives alleging they had cut short their investigation because of their close relationship with the News of the World. A group of four public figures, including former deputy prime minister John Prescott, is poised to sue police over a failure to warn them they had been targeted by the private investigator at the centre of the scandal, Glenn Mulcaire.

The Guardian has learned that the Metropolitan police commissioner at the time of the original investigation, Sir Ian Blair, was among those whose names were found in material seized from Mulcaire, raising questions about whether officers who were directly involved in the investigation had discovered that they, too, had been targets of the newspaper. It is understood Blair was assured at the time that his phone had not been hacked.

The former Labour minister Tom Watson today called on the government to set up an inquiry into the relationship between Scotland Yard and Rupert Murdoch's News Group, which publishes the News of the World. In a letter which was addressed to the deputy prime minister, Nick Clegg, in the absence of the prime minister, who is on paternity leave, Watson wrote: "The testimony given to the New York Times is that the police did not share all the relevant information with the Crown Prosecution Service, and that, if they had done, the CPS would have reached a different conclusion. These are clear grounds for a judicial inquiry.

"I think that information should be made available to the people concerned."

Amid signs of unease among the Tories' coalition partners at the new allegations about Coulson, a Lib Dem member of the Commons culture select committee has also called for an inquiry.

Adrian Sanders, MP for Torbay, said: "For the sake of justice a judicial inquiry would, along the lines of the Hutton inquiry, put this to bed once and for all."

At the end of the original police inquiry, in January 2007, Mulcaire and the News of the World's royal reporter, Clive Goodman, were jailed for illegally intercepting the voicemail messages of eight people. The Guardian last year revealed that the scandal involved other journalists at the paper and numerous other victims.

The News of the World today confirmed one of its reporters is currently suspended after his phone number was allegedly identified as the source of an unauthorised attempt earlier this year to access the voicemail of a public figure. The Guardian understands the suspended reporter has worked at the News of the World since January 2005, specialising in celebrity scoops. His name has not appeared in the paper since April. The reporter today did not return phone calls.

The paper's managing editor, Bill Akass, said it was still investigating the allegation. The Press Complaints Commission said it had been aware of the allegation since June but had chosen not to investigate because it was the subject of legal action by the alleged victim. In May the PCC's chair, Lady Buscombe, told Radio 4's Today programme: "If there was a whiff of any continuing activity in this regard, we would be on it like a ton of bricks. I can absolutely assure you of that."

Scotland Yard is facing legal action from four people whose names were found in material seized from Mulcaire in 2006 and who were not warned by police that they were potential victims. The former deputy prime minister, John Prescott, has written to them asking for an explanation for the failure. His solicitor, Dominic Crossley, said: "Absent a sufficient response, he will be beginning proceedings."

Prescott said tonight: "It's vital that the Met comes clean and reveals who and how many people were targeted by this rogue newspaper. We need to know the full truth."

The former Europe minister Chris Bryant, whose name and phone number were found in Mulcaire's possession and who was targeted by tabloid journalists, separately is preparing for a similar judicial review of the police conduct of the case.

Bryant is involved in a joint action with an investigative journalist, Brendan Montague, and one of Scotland Yard's former deputy assistant commissioners, Brian Paddick, whose name was found in Mulcaire's records but who was never warned by his own former colleagues.

Their solicitor, Tamsin Allen of Bindman, plans to ask the court to order Scotland Yard to hand over a list of all those who have been identified as potential victims. She said: "According to the rules, the claim and the pre-action letter should be served on anyone with a legitimate interest in the outcome. We say that that includes all of the people who are effected in the same way as our clients."

According to paperwork in the possession of the CPS and seen by the Guardian, Scotland Yard made repeated requests to prosecutors to "ring-fence" the evidence in order to conceal the names of "sensitive" victims. The paperwork also shows that, after studying phone records, the police found that "a vast number of unique voicemail numbers belonging to high profile individuals (politicians, celebrities) have been identified as being accessed without authority" but the officer in charge, Andy Hayman, subsequently claimed that they had found "only a handful" of victims, a claim which has been repeated by senior Yard officials in recent press briefings.

The lead Labour member on the Metropolitan Police Authority, Joanne McCart ney, tonight wrote to the Metropolitan police commissioner, Sir Paul Stephenson, asking for details of senior officers whose voicemail may have been intercepted by Mulcaire. "It is vital that the public can be confident the Met is investigating crime without fear or favour," she wrote.

Today it emerged another senior Scotland Yard officer at the time, Michael Fuller, was also on the list of names found in the private investigator's possession.

Scotland Yard has previously admitted that police officers as well as government, military and royal figures were among those who were warned they were potential victims, but they have refused to identify the individuals or even to say how many they warned.

Scotland Yard today dismissed the claims about them. "The Met does not consider the issues raised by the New York Times accurately reflect how the investigation was conducted," a spokesman said.

Other legal actions are also being launched. Sky TV football commentator Andy Gray, the former MP George Galloway, and Max Clifford's former assistant, Nicola Phillips, have all separately issued proceedings for invasion of privacy. And Mark Lewis, a solicitor who handled an earlier legal action, is suing Scotland Yard and the Press Complaints Commission in relation to remarks made in a speech made by Lady Buscombe last year. The PCC has formally apologised, but the case continues.

Others who are known to have had their voicemail accessed – but who were not identified in the original court case – include Prince William, Prince Harry, the then culturesecretary Tessa Jowell, Boris Johnson, the then-editor of the Sun Rebekah Brooks, Andy Coulson himself as editor of the News of the World, and the former England football manager Steve McClaren.