Two dead subpostmasters’ convictions were an “abuse of process”, lawyers for the Post Office have told a court amid what is thought to be a legal first over how to clear their names.

Peter Huxham was jailed and Roderick Dundee given a community service order after their respective Horizon IT accounts showed unexplained shortfalls.

The “unfair prosecutions” relied solely on records from Fujitsu’s faulty Horizon IT system, Simon Baker KC, representing the Post Office, told Southwark Crown Court – sitting at the Royal Courts of Justice.

The two men’s cases mark the first time the Criminal Cases Review Commission (CCRC), which reviews suspected miscarriages of justice, has referred a Post Office conviction of a dead person to a crown court.

But no legislation expressly exists to let a crown court hear appeals from the magistrates’ court on behalf of a dead person.

Lawyers for the two men and the Post Office agreed that the convictions should be quashed, with Mrs Justice Farbey hearing legal submissions on whether the case should be heard at the High Court rather than at a crown court.

Tim Moloney KC, on behalf of Mr Huxham and Mr Dundee, said in written submissions: “They have already waited too long for the justice which is due to them from the respondent accepting its unjust treatment of them.”

He added that the “injustice” would not be removed if their convictions were quashed by the pending legislation to automatically exonerate hundreds of wrongfully convicted subpostmasters.

“Ministers have already stated publicly that there is a risk that the legislation will lead to the quashing of convictions of people who were guilty of the crimes of which they were convicted,” he said.

“Plainly, the quashing of a conviction by the pending legislation would be grossly inadequate in these clear Horizon cases.”

Unlike the scores of former subpostmasters who have had their cases considered by the Court of Appeal, Mr Huxham and Mr Dundee’s cases need to be considered at the crown court as they were convicted at magistrates’ courts.

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Subpostmaster Mr Huxham was handed an eight-month prison sentence after he was convicted of fraud by false representation at Torquay Magistrates’ Court in March 2010.

The shortfall in his account was spotted on September 29 2009 and Mr Huxham told auditors that money had disappeared from his Post Office in Exeter.

He had been paying back the funds shown to be missing on the Horizon IT system but as the costs spiralled he started to falsify the account records.

Mr Baker read a statement provided by the auditors in 2009 which said: “He (Mr Huxham) was adamant that he had not taken the money himself.

“The only possible explanation that he could think of was a member of staff that worked in that shop.”

Mr Baker added that “had (Mr) Huxham known about the flaws in the Horizon system then it’s unlikely that he would have suspected any theft”.

Mr Dundee was a subpostmaster in Cambridgeshire when auditors spotted a £12,375.52p shortfall in his account.

He admitted to three charges of false accounting in July 2005.

At the end of Tuesday’s hearing, Mrs Justice Farbey said she would give her decision at a later date “because of the complexity in this case, which I trust may have an effect on many cases”.