The government is investigating ways to speed up the overturning of wrongful convictions of sub-postmasters affected by the Horizon scandal.

Post Office minister Kevin Hollinrake told MPs he expected to unveil a solution shortly, after holding talks with Justice Secretary Alex Chalk on Monday.

Ministers are facing fresh calls to act after an ITV drama, Mr Bates Vs The Post Office, returned the huge miscarriage of justice relating to the Horizon IT system to the spotlight.

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The show tells how former sub-postmasters and sub-postmistresses were held liable by the Post Office for financial discrepancies thrown up by its computerised accounting system Horizon, developed by Fujitsu.

Between 1999 and 2015, more than 700 Post Office branch managers were convicted after the faulty software made it look like money was missing from their shops.

Many were jailed, bankrupted and in some cases, took their own lives – but so far only 93 convictions have been overturned.

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Mr Hollinrake said he had a “very positive meeting” with Mr Chalk on Monday, where they discussed how to help the convicted branch managers clear their names.

The Post Office minister told MPs: “We have devised some options for resolving the outstanding criminal convictions with much more pace.

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“[The justice secretary] will quite rightly need to speak to senior figures in the judiciary about these options before we put them forward.”

There have been calls for the government to mass exonerate all those who were convicted and for the Post Office to be stripped of its prosecution powers.

Mr Hollinrake did not detail what solutions are under consideration but said the government “shall be able to announce these proposals to the House very shortly”.

Later, in response to a question from former justice secretary Robert Buckland, he said legislation to create a presumption of innocence for victims “is something we discussed”.

Read More:The true story behind drama on Horizon IT scandal

He also said that “proper and thoughtful consideration” will be given on how private prosecutions are undertaken “to make sure a scandal like this can never happen again”.

Mr Hollinrake also announced that former High Court judge Sir Gary Hickinbottom will chair an independent panel assessing the financial losses of postmasters with overturned convictions.

‘Real villains’ should be prosecuted

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But former Tory minister David Davis, who has said victims of the scandal should be able to submit a mass appeal, pressed for further action in the Commons.

He said on top of speeding up the exoneration process, the Post Office should be banned from “hiring expensive lawyers” to challenge compensation claims.

He also suggested the “real villains” of the scandal be prosecuted, saying “we know who they are”.

Asked if those suggestions could be achieved “in months rather than years” Mr Hollinrake said: “Yes, we want a more rapid means of overturning convictions.

“Yes, we want to make sure the Post Office doesn’t challenge unfairly any attempt to overturn convictions. Yes, in terms of making sure the investigatory process happens more quickly.”

The statement came as former Post Office boss Paula Vennells was coming under greater pressure over her CBE.

A petition to the Forfeiture Committee calling for Ms Vennells, who ran the Post Office while it routinely denied there was a problem with its Horizon IT system, to lose the honour has attracted more than one million signatures.

Earlier on Monday, Rishi Sunak signalled he would support a committee looking into the title, while Mr Hollinrake said it is “perfectly reasonable” to ask her to hand it back.

The Post Office is wholly owned by the government and a public inquiry into Horizon is ongoing.

Reports suggest that 50 new potential victims have approached lawyers since ITV’s drama was broadcast.

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Scotland Yard said on Friday that officers are “investigating potential fraud offences arising out of these prosecutions”, for example “monies recovered from sub-postmasters as a result of prosecutions or civil actions”.

The Metropolitan Police had already been looking into potential offences of perjury and perverting the course of justice in relation to investigations and prosecutions carried out by the Post Office.

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