Dozens of former sub-postmasters are to have convictions for theft, fraud and false accounting referred to the Court of Appeal.
The Criminal Cases Review Commission said it had decided to refer for appeal the convictions of 39 people from a total of 61 Post Office applicants, with further work to do on the remaining 22 cases.
The commission announced it will be referring cases on the basis that each prosecution amounted to an "abuse of process".
The sub-postmasters and postmistresses had been accused of stealing money after the Post Office installed a new, defective, computer system which showed big discrepancies in the accounts.
Some were jailed for offences including false accounting, fraud and theft, while others were made bankrupt.
Last year, the Post Office agreed to pay £58 million compensation to 550 sub-postmasters it wrongly accused of theft and false accounting and now many are trying to get their criminal convictions overturned.
Jo Hamilton was accused by the Post Office of taking £36,000 from the village shop she ran in Hampshire, and after a two-year legal battle pleaded guilty to false accounting at Winchester Crown Court in order to escape a more serious charge of theft.
"It's fabulous, the chance to clear my name and get rid of my criminal record," she told the BBC.
Helen Pitcher, who chairs the Criminal Cases Review Commission, said: "This is by some distance the largest number of cases we will ever have referred for appeal at one time.”
A Post Office spokesman said: "The Post Office has been assisting the Criminal Cases Review Commission since applications were first made to them by a number of former postmasters. We have always accepted our serious obligations and responsibilities to the commission's work.
"We have not yet received statements of reasons from the commission about the referrals they are making to the Court of Appeal. We will be looking carefully at the commission's decision when we have that information and continue to fulfil all their requirements of us.
"We have also been doing all we can to ensure that, in the light of the findings in the Horizon judgment, further disclosure is provided as appropriate in other cases where Post Office acted as prosecutor, not just those reviewed by the CCRC. The CCRC's reasoning will inform our review of these cases, which is being carried out by an external team of criminal lawyers.
"We won't be commenting on individual cases, because it would be inappropriate to prejudge the outcome of the important work that the CCRC is continuing to do or the Court of Appeal's processes."