Published Thursday, 13 December 2012
A report published on Wednesday said there was no overarching state conspiracy in the UDA/UFF shooting of Mr Finucane, who was killed at his north Belfast home in 1989.
However it found "shocking" levels of state collusion.
The 500-page report, headed up by Sir Desmond de Silva QC, was ordered by Prime Minister David Cameron in October last year, after he refused a public inquiry.
It has been criticised by the family, who dismissed it as a "whitewash" and a "sham".
Pat Finucane's son John has told UTV it may take a change of government before their hopes of a full inquiry can be met.
"It seems from the statement of the PM in the House of Commons he certainly feels that the truth has been delivered in the context of this de Silva report," he said.
Ed Miliband made Labour's position very clear in the House and I think everybody's rights will be protected in a public inquiry, no fact will now be determined unless it is rigorously challenged
"Both my family and what was very clear today is that a significant number of the House of Commons feel differently. Whether that means there will need to be a change of Government before we get an inquiry I am not sure, but one thing is for certain is that the calls for a public inquiry remain and remain very strongly."
The family have been backed by former Secretary of State Shaun Woodward, who believes the new report strengthens their position.
The Labour MP told the BBC: "What I think this report does is simply add more weight of evidence to the argument for an inquiry, not against an inquiry.
"For me the most shocking thing in this report isn't to learn that very clearly the state was involved in collusion in the murder of Pat Finucane. The most shocking part of this report is the scale of the collusion that seems to have taken place."
Mr Cameron said the murder was an "appalling crime" that happened during an "extremely dark and violent time in Northern Ireland's history".
He said the review found that the Army and Special Branch had advance notice of a series of planned UDA assassinations, but took no action.
"It should have been clear to the RUC Special Branch from the threat intelligence that... the UDA were about to mount an imminent attack but... it is clear that they took no action whatsoever to act on the threat intelligence," Mr Cameron said.
The de Silva report found that employees and agents of the state played "key roles" in the murder, and Mr Cameron said: "It cannot be argued that these were rogue agents."
The Prime Minister added: "Sir Desmond says he is 'left in significant doubt as to whether Patrick Finucane would have been murdered by the Ulster Defence Association in February 1989 had it not been for the different strands of involvement by elements of the State'."
But the de Silva review found no evidence that any Government minister was aware in advance of the murder or knew about the subsequent cover-up.
Mr Finucane's son continued: "I think the Government should do the right thing for once and announce that there will be a public inquiry.
"Here we have criticism of RUC Special Branch but we don't know exactly what process de Silva went through to come to that conclusion.
"I think we need a very public and transparent examination of what went on and then everyone will be able to see for themselves what the truth was."
© UTV News