The government is looking at ways to fast-track the appeals of hundreds of sub-postmasters caught up in the Post Office IT scandal.
More than 700 people received criminal convictions after faulty software made it look like money was missing.
To date, 93 convictions have been overturned and only 30 have finalised compensation with the government.
Business Minister Kevin Hollinrake said plans to speed up the remaining cases would be announced “very shortly”.
Mr Hollinrake said options including new legislation were being considered.
On Monday, Mr Hollinrake met Justice Secretary Alex Chalk to discuss what he called “one of the greatest miscarriages of justice in our history”.
“We have devised some options for resolving the outstanding criminal convictions with much more pace,” the minister said.
But he added, Mr Chalk would “need to speak to senior figures in the judiciary about these options before we put them forward”.
He said the pair had discussed “at length” the possibility of changing the law in order to deal with those who are still waiting to clear their names.
Between 1999 and 2015, the Post Office prosecuted 736 sub-postmasters and sub-postmistresses – an average of one a week – based on information from a computer system called Horizon.
Many maintained their innocence and said they had repeatedly raised issues with Horizon.
But some went to prison for false accounting and theft. Many were financially ruined.
The government is also looking at changing the rules round private prosecutions, after the Post Office pursued its former employees through the courts.
Campaigners called for the Post Office to be prevented from taking part in appeals against the convictions of former sub-postmasters.
The government also announced retired judge Sir Gary Hickinbottom would chair an independent panel overseeing compensation payments to those whose convictions have been overturned.
‘Keep the momentum ‘
Alan Bates, a former sub-postmaster who has led efforts for justice, told the BBC he believed a “resolution” was “closer”.
Mr Bates, played by Toby Young in a recent ITV drama about the scandal, said the years it had taken to get to this point had been “frustrating”, but added the ITV show had enabled a “broader audience” to understand what happened.
“The most important thing is for government to make sure that this financial redress goes through at speed to get it there as soon as possible, not wait, not spend money with lawyers time and time again,” Mr Bates said.
“We still have to keep the pressure on and we have got to push people and we’ve got to get the whole thing moving and keep the momentum.”
“The group has lost 60 or 70 people since we started all this. People need to get on with lives, they need to be able to draw a line under it – they will never forget it, but they have got to be able to get on and unfortunately they do need money to keep them going.
“This money is only what they are owed. This is money to put them back in a position what they would have been had Post Office not done what they did to them.”
There has also been a campaign to strip former Post Office boss Paula Vennells of her CBE over the scandal.
Ms Vennells, who was Post Office chief executive between 2012 and 2019, has been urged to forfeit her honour.
Prime Minister Rishi Sunak’s official spokesman said: “The prime minister shares the public’s feeling of outrage on this issue. He would strongly support the Forfeiture Committee if it chose to review the case.”
The Forfeiture Committee can recommend honours are stripped if a person has brought the system into disrepute.
Ms Vennells has said previously that she remained “truly sorry for the suffering caused to wrongly prosecuted sub-postmasters and their families”.
She also said she continued to fully support and focus on co-operating with the ongoing public inquiry into the scandal.
