Damian Green's arrest sparked a huge political row
A report into how the Metropolitan Police handled the arrest of MP Damian Green showed "serious failings" in police practice, the Conservatives say.
The report, by the head of the British Transport Police, concluded the arrest of Mr Green in a leak inquiry was lawful but questioned the methods used.
Conservative and Labour MPs are calling for the report to be published in full.
Mr Green was held for nine hours and had his Commons offices searched in a probe into leaks from the Home Office.
Home Office civil servant Christopher Galley was also detained on suspicion of passing leaked information to Mr Green, the party's immigration spokesman.
Both men were released on bail without charge.
Scotland Yard has revealed some of the report into the case but insists it cannot release it in full while its investigation is still ongoing.
The Met said the review of its inquiry "raises concerns" about methods but says the arrest and search of the MP's office were found to be "lawful".
But Met Assistant Commissioner Bob Quick said he would not publish the report because it related "to an ongoing criminal investigation" in which people had been arrested.
The Conservatives said the report indicated there were "very serious failings in the police operation".
"As we have said all along we believe Damian Green has done nothing wrong," said a party spokesman.
"We very much hope that this matter can now be resolved speedily."
The arrest and search of Mr Green's Commons office, including his computer, prompted a political row.
The British Transport Police were asked to look into how the police had dealt with the investigation, and their findings have now been handed to Scotland Yard.
In his statement, Mr Quick welcomed assurances in the review by BTP Chief Constable Ian Johnston that "the arrests and searches were lawful".
He said: "He recognises that there are arguments, either way, regarding proportionality over the manner of arrest of a Member of Parliament but questions the method taken in this case.
"He also raises concerns as to whether elements of the investigative approach meet current policy and best practice. These issues will be carefully considered."
He added that the review notes that police investigations can be "especially challenging when faced with Parliamentary rights and freedoms".
He said it suggests the force should work with the "relevant authorities to develop guidance to inform future decisions and actions in such circumstances".
The police's refusal to divulge the whole of the report has led to anger in Parliament.
On Tuesday evening, Conservative MPs Bill Cash and Richard Bacon raised points of order in the Commons, demanding the review be published.
Speaker Michael Martin said he would consult his advisers overnight and respond as quickly as possible.
Former shadow home secretary David Davis said the report should be published in full as quickly as possible.
He added: "This is clearly a highly critical report and should not be buried on a day when there is lots of other home affairs news."
Labour's Andrew Mackinlay also called for the report to be published in full: "Clearly it is acutely embarrassing. They are hiding behind the excuse of 'ongoing criminal proceedings'."
A promised Parliamentary inquiry into what happened is being boycotted by the Tories and Lib Dems because the government want to delay it until after the police inquiry has concluded.
Two other Commons committees, the home affairs and the public administration committees, will both examine aspects of the case.