The Post Office has appointed external investigators to examine allegations of deficiencies in the computer system used in all its outlets.
It comes after many sub-postmasters said they had been wrongly accused of theft, fraud and false accounting.
Around 100 sub-postmasters and sub-postmistresses have registered an interest in suing Post Office Ltd over its Horizon computer system.
Horizon records financial transactions in branches across the UK.
Sub-postmasters say they have been forced to pay back many thousands of pounds' worth of money which they did not take.
Many of them them were stripped of their post office contracts and bankrupted, and a handful have served prison sentences.
The Post Office has instructed a firm of forensic accountants, 2nd Sight Limited, to conduct an independent review of 10 existing cases raised by a number of MPs and the law firm Shoosmiths.
A confidential Post Office internal memo in September 2008 said that in its crown offices alone - those operated by the Post Office itself rather than by sub-postmasters - there had been £2.2m of losses in one year, which was having a serious effect on its ability to achieve profitability.
It has refused to publish figures on apparent losses at sub-post offices.
Seema Misra, a former sub-postmistress from West Byfleet, Surrey, who was convicted in 2010 of stealing nearly £75,000 and jailed for four months, said she hoped the investigation would help clear her name.
She was pregnant with her second child when convicted and lost the contract to run the post office.
She told the BBC: "My life is completely shattered. I want to get the investigation done - it was the system, or whatever it was, it wasn't my fault - and get my name cleared.
"I'm no thief, I never was. I haven't taken a single penny from the Post Office. I put money in the Post Office. I haven't taken any of their money."
The Post Office backs the conviction, saying a jury found her guilty of theft.
The Post Office has repeatedly denied there is a problem with the system, saying the claims have been made by a very small number of people who had contracts with it.
A spokesman said: "The Post Office continues to have absolute confidence in the robustness and integrity of its branch accounting processes.
"Over the past 10 years, many millions of branch reconciliations have been carried out with transactions and balances accurately recorded by more than 25,000 different sub-postmasters.
"The Post Office has no hesitation in agreeing to an external review of these few individual cases that have been raised with us by a number of MPs."
But Conservative MP Andrew Bridgen said the external investigators should have been appointed independently.
Mr Bridgen, who has such a case in his own North West Leicestershire constituency, said: "I would far rather they be appointed by another body. I would prefer it if they were paid by the Cabinet Office.
"It is important that this whole review should be beyond reproach and conducted at arm's length from the Post Office."