London's Metropolitan Police said on Thursday it would move to urgently "establish the facts" around the report.
Call for answers
The Guardian has alleged that John Prescott, Britain's former deputy prime minister, Boris Johnson, London's mayor and actors Gwyneth Paltrow and Jude Law were among those targeted in the phone hacking.
It also wrote that the News of the World had paid more than $1.6m in secret out-of-court settlements to suppress legal cases that would have revealed evidence about the scale of phone tapping.
Prescott has called on the police to investigate why action had not been taken on the suspected hacking, if it was previously known about.
"For such a criminal act not to be reported to me, and for action not to be taken against the people who have done it, reflects very badly on the police, and I want to know their answer," he said.
John Whittingdale, who heads parliament's culture, media and sport committee, said his group would hold a meeting about the report on Thursday.
"There are a number of questions I would like to put to News International on the basis of what the Guardian has reported," he said.
The practice of phone hacking by newspaper journalists was first exposed when the News of the World's royal editor was jailed in 2007, after the phone messages of aides to Prince William, the eldest son of Prince Charles and the late Princess Diana, were tapped.
Andy Coulson, the paper's editor at the time, is now director of communications for David Cameron, the opposition Conservative party leader.
He resigned from his newspaper post after Goodman was sentenced, but said he had no knowledge of the hacking.
News of the World sells 2.9 million copies every week, making it Britain's biggest-selling Sunday newspaper.