Wrongly accused subpostmasters will be given an opportunity to have their cases re-assessed, as part of an an additional independent appeals process to the Horizon shortfall scheme (HSS), the Government has announced.

More than 700 subpostmasters were prosecuted by the Post Office and given criminal convictions between 1999 and 2015, as Fujitsu’s faulty Horizon IT system made it appear as though money was missing at their branches.

Business Secretary Jonathan Reynolds told the Commons the new appeals process would be “easy” to engage with and its outcomes would be “delivered at pace”.

He added that those with “new information” will be able to access the scheme, but shadow business secretary Kevin Hollinrake argued it should be open to all subpostmasters.

In a statement on Monday, Mr Reynolds said: “As we stand and sit here today in the shadow not just of this scandal, but of Grenfell, of infected blood and several more, I know it is the firm conviction of everyone in this House that we must do better.

“This is not an issue of politics, but of justice.”

He added: “The Horizon Compensation Advisory Board recommended last year that we should introduce an independent appeals process to the Horizon shortfall scheme. Today, I am pleased to announce that we have accepted their recommendation.

“This appeals process will enable claimants who have settled their claim under the HSS to have their case reassessed with the benefit of any new information that they were not able to include in the original application.

“It will be delivered by my department in house, and we will apply the lessons learned from address schemes to date to ensure that the process is easy for postmasters to engage with and the outcomes are delivered at pace. We will announce further details in the coming months.

“There will be no obligation for postmasters to appeal their settlement, and no doubt many will be content that their claims have been resolved fairly.”

Tory former minister Mr Hollinrake welcomed the introduction of an appeals process but pushed the Government to make this available to all subpostmasters.

Mr Hollinrake said: “He confirms that the appeals process will be open for claimants who have settled their claim under the HSS, but it is restricted to those who have new evidence to support their case.

“In the same breath, he recognises lessons learned from redress schemes to date, indicating his department are aware of the flaws in the scheme, which I also acknowledge. So will the appeals process also be available, crucially, as it should be to all claimants, not just those with new information?

“Because given the accepted flaws in the scheme, it would be wrong to leave individuals without the opportunity for appeal.”

He also raised concerns that only 130 letters confirming quashed convictions had been sent by the Ministry of Justice, despite there being around 700 wrongly accused subpostmasters.

Mr Reynolds said he will consult with subpostmasters to “make sure the eligibility criteria are correct” before the scheme begins in “a matter of months”.

He added that 180 subpostmasters have been sent letters which tell them that their convictions have been quashed.

Former chair of the business and trade committee, Liam Byrne, said second offers – which occur when an initial compensation offer is rejected – are taking “far too long”.

The Labour MP for Birmingham Hodge Hill and Solihull North said: “So the claimant’s lawyers have got a fixed amount of time to put in a claim, where it is then contested it is taking far, far too long… to come back and provide a second offer.”

In response, Mr Reynolds said the Government is committed to issuing offers to 90% of initial claims within 40 working days.

Elsewhere in the session, Mr Reynolds said the Post Office’s business model was not fit for purpose.

He said: “The public support for the brand, for the people on the front line, I think is very strong, but the business model as it stands is not one that is fit for purpose.

“I think postmasters deliver essential services, but they don’t make enough money from those essential services. I think the money they make, too much of that goes into the centre, and doesn’t return to the front line in a way that is a viable business model for all of our constituencies.

“And these issues of how as an organisation, the Post Office functions have to be tied, not just culturally, to the reforms and the redress that we’re all seeking to deliver, but to the business model as well.”