A call has been made for hundreds of Post Office staff wrongly accused of theft and false accounting to all have their convictions overturned.
More than 700 Post Office managers were convicted when faulty accounting software made it look as though money was missing from their sites.
A board overseeing compensation said until all convictions were quashed, “we cannot put the scandal behind us”.
The Ministry of Justice said it would respond in due course.
The Horizon scandal – named after the faulty accounting software – constitutes Britain’s most widespread miscarriage of justice.
The convictions of hundreds of postmasters and postmistresses for false accounting and theft between 2000 and 2014 resulted in some people going to prison.
Many were financially ruined after being prosecuted and some of those wrongly accused have since died.
In September, the government said Post Office staff who have had wrongful convictions for theft and false accounting overturned would be offered £600,000 each in compensation.
But so far, only 93 convictions have been overturned, according to the Horizon Compensation Advisory Board, an independent group overseeing compensation related to the scandal.
Chris Hodges, chair of the board, said they believed more than 900 postmasters had been prosecuted in relation to the faulty Horizon software.
“Many victims remain traumatised and ostracised by their communities,” he said in a letter to the Lord Chancellor Alex Chalk.
He said while individuals could apply to have their convictions overturned, the small number of cases meant the “current approach is not working”.
Reasons for this, Prof Hodges added, included an unwillingness of people to appeal due to a “deep distrust of authority”, evidence being lost or destroyed, and issues with compensation if a Post Office manager is not granted a retrial.
“The convictions are unsafe not only because they relied on the Horizon computer evidence, but also because of egregious systemic Post Office behaviour in interviews and pursuing prosecutions,” he said.
“This led to guilty pleas and false confessions, driven by legal advice to victims to minimise sentences, and by the psychological pressure of dealing with an institution systematically disregarding the truth and fairness.”
Prof Hodges said the “only viable approach” was for “all 900+ Post Office-driven convictions from the Horizon period” to be overturned.
“A small minority of these people were doubtless genuinely guilty of something. However, we believe it would be worth acquitting a few guilty people (who have already been punished) in order to deliver justice to the majority – which would not otherwise happen,” he said.
A Post Office spokesperson said: “We strongly encourage people who believe they were wrongly convicted, for any reason, to consider an appeal.”