The families of 96 Liverpool fans who died at Hillsborough in 1989 hailed the announcement yesterday that an application has been lodged by the attorney general to have the original inquests into the disaster quashed in the high court.

A judge will rule on the application, which comes after the Hillsborough Independent Panel in September discredited the original inquest's principal findings and revealed a coverup that attempted to shift the blame on to the victims, but the bid is considered likely to succeed.

Dominic Grieve, the government's chief legal officer, said there was a "good" case for setting aside the accidental death verdicts and holding new hearings into the deaths of supporters.

Should the court decide to quash the original inquests and order fresh ones to be heard, its powers are limited to referring the cases back to the district in which they were originally heard, which means sending them back to Sheffield or Doncaster in 95 of the cases. It is understood that the attorney general will suggest that the court should return the cases to Doncaster, as the families themselves have made it clear that they do not want the inquests heard in Sheffield.

Grieve said that the principal ground for the application is the new medical evidence, adding: "The alteration to police and emergency services evidence is a supporting factor, as is stadium safety."

The chairwoman of the Hillsborough Family Support Group, Margaret Aspinall, whose son James, 18, died in the tragedy, said: "We have waited over 20 years for these verdicts to be overturned and I'm sure all the families will be delighted to hear that these steps are being taken."

The attorney general's office also said yesterday that the application drew on additional analysis provided by Dr Bill Kirkup CBE, the medical adviser on the panel, who has said up to 41 of the 96 fatalities might have been saved with quicker treatment.

The families, who have expressed the wish that the new hearings should take place in Liverpool, will have a number of priorities in mind. They will be looking for a precise account of how each person died and, ultimately, verdicts of unlawful killing.

The families have always felt desperately aggrieved by the fact that the coroner who presided over the original inquests limited evidence to 3.15pm on the day of the disaster – based on the assumption that all of those who died were already irrecoverably injured by then – and have bitterly contested the way in which the original inquest was conducted, leading to the verdict of accidental death.

Campaigners such as Anne Williams, whose son Kevin died in the disaster, have always contested the account given at the inquest that he died from traumatic asphyxia and so could be considered irrecoverable by 3.15pm on the day of the disaster.

She wrote on Twitter yesterday: "Just received email the attorney general is sending Kevin's case to the divisional courts seeking a new inquest his death."

More than 105,000 people have signed an e-petition calling for a fresh inquest into her son's death to be held swiftly as Anne is suffering from cancer.

She has has made four submissions to overturn the verdict of her son's inquest to different attorney generals over the years, and said that the announcement was what she had been waiting 23 years for. "Looking at [the email] now, I can't believe it," she said. "This is my fourth submission to attorney generals over the years and they have always come back, 'Not in the interests of justice'."