In a double defeat for the Government, peers voted by 238 votes to 209 – a majority of 29 – for the go-ahead to part two of the Leveson Inquiry into the conduct of the press.
They also voted by 211 votes to 200, a majority of 11, for another amendment to the Government’s Data Protection Bill, which would make newspapers face big bills in data protection disputes.
Under this proposal, newspapers not signed up to a state-supported regulator would have to pay their own and their opponent’s legal costs, even if they were successful in court.
But immediately after the Government defeats, which had been widely predicted, Mr Hancock pledged to attempt to overturn them in the House of Commons.
“House of Lords have just voted to restrict press freedoms,” he tweeted.
“This vote will undermine high-quality journalism, fail to resolve challenges the media face and is a hammer blow to local press.
“We support a free press and will seek to overturn these amendments in the Commons.”
But Labour’s deputy leader Tom Watson, the shadow culture secretary, said the Lords’ vote was an “important step towards justice”.
He said: “In 2012, all parties made a promise to the victims of phone hacking.
“At many times since then the Tories have tried to renege on that promise.
“Unlike the Tories, Labour has always stood by the victims of hacking and press intrusion with promises in each of our past manifestos to enact all the recommendations of Leveson.
“These votes send a signal to the Tories: that they must keep their promises.”
The first amendment to the Data Protection Bill, requiring the Government to hold a public inquiry into “corporate governance and management failures” in the press, was moved by Baroness Hollins, who said her family have been a victim of press intrusion.
Lady Hollis said her eyes were opened to “inaccurate, corrupt and illegal practices” in the press after her daughter Abigail Witchalls was left paralysed after being stabbed in 2005.
The independent crossbench peer, a professor of psychiatry, gave evidence in the first Leveson Inquiry – set up by David Cameron in 2011 after the phone hacking scandal – accusing the press of intrusion into her family life following the incident.
Speaking of her own experience, she said one of the consequences of having data stolen was that she had started to suspect people she knew of speaking to the media.
“I stopped trusting people, even people in my own family, my neighbours and my best friends,” she said.
“I did not trust them. I did not know about hacking and blagging.”
But Tory peer Lord Black of Brentwood, executive director of the Telegraph Media Group, noted the amendment on Leveson 2 did not mention the police or politicians and that the “target is four-square the press”.
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He argued a further costly inquiry was “completely unnecessary because there genuinely is nothing left to unearth”.
“The spectre of yet another inquiry is a toxic threat to a free and independent press,” he added.