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By Karen Hoggan
Business reporter, BBC News
Former Post Office boss Paula Vennells has been accused of making a "false statement" about the outcomes of sub-postmasters' court cases.
The inquiry into the Horizon IT scandal heard Ms Vennells wrote to a government minister in 2012: "In every instance, the court has found in our favour."
Counsel to the inquiry Jason Beer KC said: "It's just not true."
Ms Vennells has been asked to comment and previously said she was co-operating with the inquiry.
She is due to give evidence to the inquiry in May.
On Wednesday, the inquiry heard that in a 2012 letter to MP Oliver Letwin, Ms Vennells wrote: "In some cases, which are fortunately very few and far between, we have had to prosecute sub-postmasters for theft or false accounting and provide evidence which substantiates our legal position.
"In every instance, the court has found in our favour."
Counsel to the inquiry Jason Beer KC said: "Now, that's a false statement there, that in every instance the courts have found in our favour. It's just not true."
He asked Lord Arbuthnot if he would have known at the time that it may have been a false statement, to which he replied: "No, I wouldn't."
Lord Arbuthnot added that he would have accepted the statement at face value and would have expected public officials such as Ms Vennells would tell the truth.
In an earlier statement to the press, Ms Vennells said: "I continue to fully support and focus on co-operating with the inquiry and it would be inappropriate for me to comment further while it remains ongoing."
Between 1999 and 2015, hundreds of sub-postmasters were wrongly prosecuted by the Post Office due to faulty Horizon software, which showed errors that did not exist.
Some lost their jobs, businesses and homes. Many were left financially ruined. Others were convicted and sent to prison and some died while waiting for justice.
At Wednesday's hearing, Mr Beer also asked Lord Arbuthnot whether Post Office officials had disclosed a long list of cases which found bugs within the IT system, and listed a number of specific cases in which postmasters had been acquitted. Lord Arbuthnot answered: "No."
'Brush off'
Earlier, Lord Arbuthnot, a former Conservative MP, said he had received the "brush off" from Ms Vennells in a letter she wrote to him defending the Horizon IT system.
The inquiry was told how in December 2011, Lord Arbuthnot wrote to the Post Office and the government saying the situation with the Horizon IT system had not been rectified and needed further investigation.
He received a response the following month from Ms Vennells in which she said there was "no evidence to support any of the allegations [from former sub-postmasters]"
"We have no reason to doubt the integrity of the system, which we remain confident is robust and fit for purpose," the letter from Ms Vennells said.
In his witness statement, Lord Arbuthnot described that as being "given the brush off".
"At this stage I did not know the truth of the matter but it was clear that a detailed investigation was needed," he said.
'Transparently honest'
Lord Arbuthnot first got involved with the sub-postmasters' cases in 2009, when he met former sub-postmaster Jo Hamilton at a constituency coffee morning.
During that year, he became aware of some reporting on the scandal and a second case in his own constituency.
Since then, he has continued to speak out on behalf of victims and sits on the Horizon Compensation Advisory Board, which advises the government financial redress for those affected.
"The sub-postmasters I had met seemed to me to be transparently honest," he said in his witness statement to the inquiry. "I do not remember anyone suggesting to me that the introduction of a new computerised accounting system had uncovered previously hidden fraudsters.
"If they did I would have given it little credence, both because of the self-evident honesty of the sub-postmasters I had met and because of the sudden rash of similar allegations appearing shortly after the installation of a new computer system, an exercise which inevitably will have teething problems.
"I was therefore not satisfied with the brush off I was getting by way of reply to my letters."
In another letter seen by the inquiry on Wednesday, Ms Vennells denied there were any problems with Horizon, saying it had been "rigorously tested".
She wrote: "The Post Office takes very seriously any perception that there is an issue with the accuracy of the Horizon system: there isn't.
"The Horizon system has been rigorously tested using independent assessors and robust procedures."