A fresh inquest into the Hillsborough disaster is likely to be ordered after the full scale of the establishment cover-up over the 1989 disaster was revealed for the first time.

Criminal prosecutions of key figures are also possible after the Hillsborough Independent Panel – which was chaired by the bishop of Liverpool, James Jones, and had unrestricted access to 450,000 documents over three years – revealed the depth of a police cover-up that swung into action the morning after the disaster.

It confirmed Lord Justice Taylor's key finding in August 1989 that the main reason for the disaster was a "failure in police control".

But it also revealed that "multiple failures" in other emergency services and public bodies contributed to the death toll. Similarly, serious failings in the inquests and reviews that followed prolonged the agony of the families of the victims.

Legal representatives for the families of the 96 victims crushed to death at the Leppings Lane end of the ground said that South Yorkshire police, Sheffield city council and Sheffield Wednesday FC could all face charges for corporate manslaughter.

Meanwhile, the attorney general, Dominic Grieve, will decide in the coming weeks whether to order a new inquest after the original, which recorded a verdict of accidental death, was found by the panel to be severely lacking.

"If David Cameron means what he says and justice has to follow truth, then they have a responsibility today to assess not just the question of unlawful killing but the cover-up and the perversion of the course of justice," said Michael Mansfield QC, who is acting on behalf of the Hillsborough Family Support Group (HFSG).

The panel discovered that as many as 41 victims of the disaster on 15 April 1989 might have been saved had the emergency response been better. They also found that 116 of the 164 police statements taken afterwards were doctored to show the police in a better light, and that the South Yorkshire ambulance service had also altered statements to deflect criticism.

An earlier inquest by Dr Stefan Popper had controversially imposed a cut-off time of 3.15pm which, said the report, "led to the mistaken belief that an effective emergency services intervention could not have saved lives".

The coroner ordered that blood alcohol levels be taken for each of the deceased. The panel found that the weight placed on alcohol levels was "inappropriate and misleading" and the pattern of alcohol consumption "unremarkable".

The report says blood alcohol levels were taken from survivors for no apparent medical reason and that attempts were made to "impugn the reputation of the deceased" by checking whether they had criminal records.

"What was new and a shock was how many of them could have been saved. That is the most important thing. I'll go home and wonder if James was one of them," said Margaret Aspinall, chair of the HFSG, whose son James was 18 when he died.

"They were the liars and we were the truthful ones, we were the innocent. To hear that apology doesn't make us feel better. We will always be the losers at Hillsborough," she said.

The prime minister, David Cameron, said in the Commons he was "profoundly sorry" on behalf of the government for what was immediately described by the former lord chancellor Charles Falconer as "a concerted conspiracy to withhold the truth" over a disaster that claimed the lives of 96 men, women and children, 80% of whom were under 30.

Cameron said: "With the weight of the new evidence in the report, it's right for me today as prime minister to make a proper apology to the families of the 96. On behalf of the government, and indeed of our country, I am profoundly sorry that this double injustice has been left uncorrected for so long."

Falconer, who is also advising the families, said he expected the attorney general to order a new inquest into the deaths:. "It is absolutely clear there is no other step he can take," he said.

The panel, constituted in 2009 on the initiative of the then Labour ministers Andy Burnham and Maria Eagle and in the wake an articleby the Guardian's David Conn, found that 116 of 164 statements supplied by South Yorkshire police in response to the disaster were changed to "remove or alter comments directly unfavourable to South Yorkshire police". In the days after the disaster, a narrative took hold that drunken Liverpool fans had caused the disaster by forcing a gate open. Allegations were printed that Liverpool fans had pickpocketed the dead and hampered rescue attempts in an infamous Sun front page headlined "The Truth", which led to a boycott of the paper on Merseyside that continues today. The Sun editor at the time, Kelvin MacKenzie, on Wednesday offered "profuse apologies" for the first time.

The panel found that the origin of untrue claims was a Sheffield news agency informed by four senior South Yorkshire police officers, a South Yorkshire Police Federation spokesperson and a local MP, Irvine Patnick.

The day the Sun allegations were published, the report describes a meeting of the South Yorkshire police federation in the Pickwick restaurant in Sheffield.

At the meeting, the chief constable, Peter Wright, who died last year, said officers should not talk to the media and should "prepare a rock solid story". He said the force needed to take control of the narrative presented to the inquiry and that "if anybody should be blamed, it should be the drunken, ticketless individuals".

"When you get the chief constable sitting down with his trade union to cobble together a solid story, then you know we've reached a new depth of depravity," said Trevor Hicks, who lost two daughters, Sarah and Victoria, at Hillsborough and is president of the HFSG.

"There were two disasters at Hillsborough. The one on the day and the one afterwards. It was not only a disaster, it was a contrived, manipulated, vengeful and spiteful attempt to shift the blame."

The 395-page report also outlines the extent to which repeated warnings over the safety of the ground were ignored and uncovers a Health and Safety Executive report that found neither the club nor the council had heeded warnings from a series of near misses in previous years.

Hicks also called on Norman Bettison, the current chief constable in West Yorkshire, to resign. He has consistently denied being involved in the operation to smear Liverpool fans, but the panel found that he was involved.

Falconer admitted that the families and the survivors of Hillsborough had been failed by "successive governments including the one of which I was a part".

In documents disclosed to the panel, the then prime minister, Margaret Thatcher, was briefed that "the defensive – and at times close to deceitful – behaviour by senior officers in South Yorkshire sounds depressingly familiar".

While there was no direct evidence that Thatcher or the cabinet was complicit in a cover-up, it is revealed that the primary concern of the government at the time was the impact of the disaster on its proposed football spectators bills.