The prime minister has said he has “full confidence” in the commissioner, despite criticism in a damning report accusing her force of “institutional corruption”.
Findings published eight years after the probe was commissioned by Theresa May said corruption and the “irretrievable” loss of evidence prevented the culprits from being brought to justice.
An independent panel said that although its investigation exposed historic failings stemming from the 1987 killing, the term institutional corruption was used “in the present tense”.
It criticised the current Metropolitan Police leadership, including the commissioner, for slowing down its work by failing to give prompt access to necessary records and computer systems.
Baroness Nuala O’Loan, chair of the Daniel Morgan Independent Panel, said Dame Cressida’s refusal to allow “proper access” to the Holmes computer investigation system hampered the inquiry.
“It caused major delays to the panel’s work, which inevitably added to the panel’s costs, caused further unnecessary distress to the family of Mr Morgan,” she added.
Baroness O’Loan said Scotland Yard’s leadership had not acknowledged or confronted its failings and showed a “lack of candour”.
“We believe the Metropolitan Police’s first objective was to protect itself,” she told a press conference on Tuesday.
“They were not honest in their dealings with Mr Morgan’s family or the public. The family and the public are owed an apology.”
Alastair Morgan, Mr Morgan’s brother whose campaign for justice led to the report, said the commissioner should “consider her position”.
He added: “She has made it very difficult. Whether she should resign? I think certainly we need much better leadership than she has provided here.”
His partner, Kirsteen Knight, told a press conference that Dame Cressida, who was appointed as commissioner in 2017, was ”no worse than any of the other commissioners that we've had to deal with“.
The home secretary told MPs she had written to the commissioner requesting a “detailed response” to the panel’s recommendations, and asked HM Inspectorate of Constabulary to look at the issues raised.
Dame Cressida, who is Britain’s most senior police officer, holds her position for a fixed term that is due to expire next spring.
The panel said Dame Cressida, then an assistant commissioner, was the “senior officer in the Metropolitan Police with responsibility for supporting the panel’s work” when it was set up in 2013.
She drew up the terms of reference for the review alongside Crown Prosecution Service officials and was involved in an initial row over “sensitive” material.
After that was resolved, the panel said it wanted access to the Metropolitan Police’s Holmes computer system but the report said Dame Cressida “expressed a strong reluctance”.
A specialist member of the panel was given access to Holmes in February 2015, but the debate continued while Dame Cressida was on secondment to the Foreign Office for two years.
Scotland Yard later allowed a Holmes terminal to be set up at the panel’s office, and then remote access during the coronavirus pandemic.
Baroness O’Loan said the panel had “never received any reasonable explanation for the refusal over seven years by Cressida Dick and her successors to permit proper access to the Holmes accounts”.
The chair said the access requested by the panel would have enabled its work to be carried out “far more efficiently and effectively”.
She said the eventual £16m cost of the probe would have been lower if not for the time delays and “very significant resources that had to be spent challenging the continuing Metropolitan Police assertions about the difficulties of enabling the requested access to the Holmes system. This should not have happened.”
At a press conference later on Tuesday, assistant commissioner Nick Ephgrave said his superior did not have “any need to consider her position”.
“She has overseen disclosure to a level that has never been done before,” he added.
“The access the panel have had has been unparalleled in my experience.”
Dame Cressida did not appear at the press conference but issued a written statement saying the failure to bring Mr Morgan’s killers to justice was a “matter of great regret”.
“Our mistakes have compounded the pain suffered by Daniel’s family - for that I apologise again now,” she added.
The commissioner insisted she had been “personally determined that the Met provided the Panel with the fullest level of co-operation in an open and transparent manner, with complete integrity at all times.”
She added: “I recognise this is a powerful and wide-ranging report. We will take the necessary time to consider it and the associated recommendations in their entirety.”
The Metropolitan Police has commissioned a new forensic review of evidence in the case to look for new opportunities, and is offering a £50,000 cash reward for information leading to the successful prosecution of those responsible for the murder.