It is calling for extra resources for the police investigation so new hacking victims can be informed more quickly.
The prime minister is due to make a statement to the Commons later.
David Cameron will speak at the start of an all-day debate on the latest developments in the hacking scandal - for which Parliament has been recalled from its summer recess.
While the MPs' report blames News International for obstructing the Met's first inquiry into hacking, it says there was no "real will" on the part of Scotland Yard to tackle the news group's failure to co-operate.
Thousands of victims It says the conduct of former Assistant Commissioner Andy Hayman, who oversaw the investigation, was unprofessional and inappropriate.
The report questions whether Mr Hayman should ever have been appointed to his role as head of counter-terrorism and says it is "deplorable" that he began working for News International two months after he left the Met.
In other developments:
- The protester accused of throwing a paper plate of shaving foam at Rupert Murdoch as he gave evidence to the Commons media select committee has been charged with a public order offence. Jonathan May-Bowles, 26, will appear before City of Westminster Magistrates Court on Friday
- Shares in News Corporation rose by 6% at the close of trading in New York after Rupert and James Murdoch's appearance in front of the committee
- Reuters reported that, in an e-mail to staff, News Corporation chairman Rupert Murdoch had said the organisation was taking "urgent steps to address the past and ensure that serious problems never happen again", and that "those who have betrayed our trust must be held accountable under the law"
- The law firm hired by News International in 2007 to review allegations of phone hacking says it is being prevented from responding to "inaccurate" comments made by James Murdoch. Mr Murdoch said a letter written by the law firm made executives at News International believe that hacking was a "matter of the past". Harbottle and Lewis says it is not being allowed to breach client confidentiality
- Australian Prime Minister Julia Gillard says the Australian arm of News Corp will have to answer "hard questions"
- Culture Secretary Jeremy Hunt tells the BBC that News Corp will have to address why so much malpractice happened in the organisation without Rupert Murdoch knowing
The committee says it is "shocked" by the way Mr Fedorcio hired Mr Wallis and says he tried to deflect blame onto a senior officer, former Assistant Commissioner John Yates.
A new police investigation, Operation Weeting, is well under way, but the MPs say unless it has more staff it could be a decade before all the thousands of possible victims are informed.
The committee praised Deputy Assistant Commissioner Sue Akers' decision to contact all potential victims of phone hacking by the NoW, but said they were "alarmed" that only 170 had so far been informed.
The committee launched its investigation into hacking last September.
Chairman Keith Vaz said the major shortcoming by the police was that victims were not put at the heart of the investigation.
Meanwhile, Mr Cameron arrived back in the UK on Tuesday night, having cut short his trip to southern Africa.
He has been briefed on the evidence given to Commons committees by News Corporation's Rupert and James Murdoch and Rebekah Brooks as well as former Metropolitan Police commissioner Sir Paul Stephenson and Mr Yates who both resigned from Scotland Yard this week.
In his statement to the Commons the prime minister is expected to give more details of the judicial inquiry he has set up and to explain efforts to be more transparent about meetings with newspaper executives.
BBC political correspondent Carole Walker said he was likely to come under pressure from Labour over new evidence that his chief of staff Ed Llewellyn prevented information about hacking allegations being passed on.
Labour said it was a deeply troubling development but the cabinet secretary said the chief of staff had acted entirely properly.