Legal advisers to the families of the 96 victims of the Hillsborough disaster have called on South Yorkshire police and Sheffield Wednesday Football Club to admit their culpability in order to avoid prolonging their agony if, as expected, a new inquest is ordered.

The attorney general, Dominic Grieve, will decide within the next six to eight weeks whether to apply to the high court for the original verdict of accidental death to be quashed in the light of the evidence contained in the report of the Hillsborough Independent Panel.

The report found that up to 41 of the victims of the 1989 disaster could have survived beyond the 3.15pm cut-off point beyond which it was wrongly assumed by the original coroner, Dr Stefan Popper, that all had been critically injured.

The report, published on Wednesday, laid bare the extent of the police cover-up following the disaster and found "no evidence" for the slurs made against Liverpool fans in its immediate aftermath as the police sought to deflect blame for their own failings.

Charlie Falconer, the former lord chancellor who is helping to advise the Hillsborough Family Support Group, said there would be no other option than to open a new inquest into all 96 deaths.

He said it would be for the coroner to decide how to proceed. But one option would be to come to a new verdict for all 96, but take new evidence only on those individuals who may have survived beyond the 3.15pm cut-off point.

The panel found there was "clear evidence" that 28 of those who died did not have traumatic asphyxia and it may have taken longer to be fatal.

There was separate evidence that the heart and lungs of 31 victims had continued to function after the crush and that was for a prolonged period in 16 of the cases. Some featured in both groups, but in all 41 victims fell into one or both category.

Falconer said the extent to which any new inquest proved a painful new ordeal for the families would be determined largely by whether South Yorkshire police and Sheffield Wednesday Football Club tried to defend themselves against the conclusions in the report.

"The size and scope of the inquest would depend on whether there was an adversarial position from the South Yorkshire police and Sheffield Wednesday. If they acknowledge it's their fault, it will be a shorter process."

Michael Mansfield QC, who is also advising the families and will meet with them on Sunday to help decide their next move, also said that there would have to be a new inquiry for all 96 victims if the existing inquest verdict was struck out.

He said that the inquest could proceed in parallel with a review by the director of public prosecutions with a view to deciding whether to bring charges of manslaughter or perverting the course of justice.

That process is expected to take between six and nine months.

Margaret Aspinall, the chair of the HFSG, said she was very confident that the existing verdict would be struck out.

"What is a shock to all the families and the thing I woke up this morning thinking about was when we found out how many could have survived beyond 3.15pm. That's nearly half of the people. That is the thing," said Aspinall, who lost her 18-year-old son James in the disaster.

She said that Wednesday had been a "historic" day but lamented that it had taken 23 years to reach the truth and for those in positions of power to be accountable.

Aspinall said that it would be difficult for some families to relive the details of the disaster in a new inquest but the vast majority were determined to have the original verdict struck out.

Falconer said that it should be possible to apply to the high court for the inquest to be heard in Liverpool rather than Sheffield.