Mr Morgan was killed with an axe in the car park of the Golden Lion pub in Sydenham, southeast London on 10 March, 1987.
A panel looking at how the Met Police handled the investigation was due to publish its findings on Monday 17 May.
However, it was halted by the Home Office who said it wanted to review the document, that was expected to contain “a sizeable chapter” on police corruption.
Mr Morgan’s family said the delay was a “kick in the teeth” and served only to “betray and undermine the very purpose of the panel”.
The Daniel Morgan Independent Panel said it had been told a publication date would not be agreed until the Home Office reviewed the report to ensure it complied with human rights and did not compromise national security.
Despite five police inquiries and an inquest, no one has been brought to justice over the father-of-two’s death, with the Metropolitan Police admitting corruption had hampered the original murder investigation.
In 2013, then home secretary Theresa May announced that an independent panel was being set up to examine the case.
The panel’s remit was to address questions relating to the murder including police handling of the case, the role corruption played in protecting his killer, and the links between private investigators, police and journalists connected to the case.
In a statement Mr Morgan’s family said: “The Home Secretary’s intervention is not only unnecessary and inconsistent with the panel’s independence.
“It is an outrage which betrays her ignorance – and the ignorance of those advising her – with regard to her powers in law and the panel’s terms of reference.
“It also reveals a disturbing disregard for the public interest in safeguarding the independence of the panel and its report.
“For us as the family of Daniel Morgan, the Home Secretary’s belated and unwarranted interference in this process is simply unacceptable.”
The panel said that it had expected its report to be tabled in Parliament by the home secretary on Monday.
But it had been advised that the period of mourning after the Duke of Edinburgh’s death and the elections had caused a backlog of matters to be placed before Parliament.
The panel said that the Home Office had not mentioned there was a need to review the report and that it had worked with its counsel to ensure it complied with the relevant legal obligations including the Human Rights Act.
It also said that the the role of the Home Secretary was limited to reporting to Parliament on the panel’s work, receiving its report, laying it before Parliament, and responding to its findings.
The panel said it was “disappointed”, but hoped the issue could be resolved so the report can be published in May.
A Home Office spokesperson said Priti Patel had an obligation to make sure the report complied with human rights and national security considerations.
They added: “Under the terms it was commissioned in 2013, it is for the Home Secretary to publish the report which she hopes to do as soon as possible.
“The Home Secretary also has an obligation to make sure the report complies with human rights and national security considerations.
“This has nothing to do with the independence of the report and the Home Office is not seeking to make edits to it.
“As soon as we receive the report, we can begin those checks and agree a publication date.
“The Home Secretary fully supports the family first approach and is hoping to meet them to discuss the report and its findings in person.”
Additional reporting by PA