It follows allegations that ex-private investigator John Ford targeted politicians using 'blagging' techniques to obtain information for The Sunday Times.
Labour's deputy leader said the claims proved that 'too many questions remain unanswered' over press intrusions.
He urged Culture Secretary Matt Hancock to reconsider his position on Leveson Part 2, which which was due to look into unlawful conduct within media organisations before being scrapped earlier this month.
Asking an urgent question in the Commons, Mr Watson referred to the allegations made by Mr Ford and said: "The second part of the Leveson inquiry could establish where the truth lies.
"That is what it was set up to do. But the Government is closing down the public inquiry before it has done its work."
The West Bromwich East MP added: "The Secretary of State is capitulating to the press barons who want to use their raw power to close down a national public inquiry.
"Is it not now clear...that too many questions remain unanswered to justify this decision to break David Cameron's solemn promise to the victims of press abuse."
Mr Hancock said the alleged activity involving Mr Ford 'apparently stopped in 2010 before the establishment of the Leveson inquiry'.
He said 'this sort of behaviour' was covered in the initial inquiry and added: "Anyone who has committed a criminal offence should face the full force of the law.
"The future of a vibrant, free and independent press matters to us all. We are committed to protecting it.
"We want to see the highest standards, and we must face the challenges of today to ensure Britain has high quality journalism, and a high quality discourse to underpin our democracy for the years to come."
Mr Ford said he targeted politicians including Tony Blair and Gordon Brown when they were in government through 'blagging' – pretending to be a bank or utilities account holder to get information.
The Sunday Times said it 'strongly rejects' the claim that it had ever commissioned anyone to act illegally.