In a letter to the Director of Public Prosecutions, High Court judge Mr Justice Fraser said that expert witnesses who gave evidence at criminal trials were aware of problems with the Horizon system, but failed to disclose them.
The Metropolitan Police force has now launched a criminal investigation into evidence given by former Fujitsu staff Gareth Jenkins and Anne Chambers during previous trials.
Last month it emerged that four former post office workers from the West Midlands, who were jailed because of shortfalls caused by a bug in the Horizon system, will now have their convictions quashed.
Rubbina Shaheen, 55, from Shrewsbury, Tracy Felstead, 38, from Telford, Neelam Hussain, 32, who kept a post office in West Bromwich, and Carl Page 54, who kept a branch in Rugeley, were told the Post Office would not be contesting appeals against their convictions.
They all say they were wrongly jailed because of financial discrepancies caused by the Post Office’s computer database.
The Court of Appeal has been told that police were to examine whether Mr Jenkins, now 68, and Mrs Chambers, 63, should face prosecution for possible perjury charges relating to evidence they had given.
The perjury allegations do not relate to the trials of any of the West Midlands staff.
Mrs Shaheen, who kept Greenfields Post Office in Shrewsbury, was jailed for 12 months in 2010 for false accounting in relation to an alleged £40,000 shortfall.
Miss Felstead, who was an 18-year-old counter clerk at the time of her arrest, was jailed for six months in 2001 after being convicted of stealing £11,500.
Mrs Hussain was jailed for 21 months in 2011
In his letter, which was released to the court last week, Mr Justice Fraser told the Director of Public Prosecutions Mr Max Hill: "I consider important evidence given both to the Crown Court and the High Court on previous occasions, in other cases, was not true, and was known not to be the truth, the whole truth and nothing but the truth, at the time it was given.
"The documents clearly show that Fujitsu knew about the existence of bugs, errors and defects in Horizon from a very early stage in the life of the system. The earliest bugs occurred and were known about in 1999."
The hearing to formally decide whether to quash the convictions is due to begin in the Court of Appeal on March 22.