Victims of the Post Office Horizon scandal whose convictions are being quashed by emergency legislation can now apply for compensation of £600,000 or more through a new scheme.

Ministers said they hope the efforts towards redress will begin to “right the wrong” of one of Britain’s worst miscarriages of justice.

Subpostmasters with overturned convictions will begin to receive letters confirming their exoneration this week, the Department for Business and Trade (DBT) said.

However, some may receive a request to “submit further information” if there is “insufficient evidence” to show it should be quashed, according to the department.

Hundreds are still awaiting full compensation after the previous government announced in January that they would be eligible for £600,000 payouts.

They can now either accept that settlement as part of the new Horizon Convictions Redress Scheme, or, if they believe their losses exceed that amount, can choose a full claim assessment route.

Business Secretary Jonathan Reynolds said he hopes the offer brings “some relief” to postmasters who have “suffered immeasurably” and waited “far too long” for the money.

Justice Secretary Shabana Mahmood said: “Justice must be a reality, not an ideal. Today we begin putting this into practice by overturning the convictions of the innocent postmasters affected by this inexplicable and unprecedented miscarriage of justice.”

But opposition critics hit out at the pace of progress, with shadow business secretary Kevin Hollinrake saying only 10 confirmation letters had been sent out so far before the Commons rises for recess.

“It is disappointing that I’ve again had to ask an urgent question to get the Government to come to the despatch box,” he said, facing business minister Justin Madders in the Commons on Tuesday.

“This is a, very clearly, important matter and one deserving of full scrutiny by this House, and, despite earlier promises by him only 12 days ago to give the House a significant update, only a written statement was available.”

Mr Madders said he understood Mr Hollinrake’s “frustration” but pointed to challenges slowing the Government’s pace, including in accessing court documents that sometimes stretch back decades.

“I understand when the shadow secretary of state made that promise (for Horizon redress by the summer recess) as a minister, he did so in good faith, but it has turned out that there have been additional physical checks that have been required,” he replied.

Some 89 people have already registered for the scheme as of Tuesday morning after applications opened online, he added.

The scheme was designed to redress victims whose convictions had not already been overturned in the courts and includes those whose names were cleared by blanket legislation introduced by the previous government.

The Post Office Offences Act enabled postmasters wrongfully prosecuted of swindling from their branches after faulty accounting software made it seem as if money was missing to be exonerated without a lengthy court process.

The case is seen as one of the greatest miscarriages of justice in British legal history.

Lawyer Neil Hudgell, whose firm Hudgell Solicitors has represented former subpostmasters during the public inquiry into the scandal, said he is “confident” the Government recognises the challenges faced by victims.

Mr Hudgell, whose firm is advising around 170 people eligible for the new scheme, said: “I warmly welcome the launch of the new scheme and we have more than 170 exonerated postal workers signed up today for us to assist them with their claims as the scheme opens for business.

“We have had many meetings with Government and the Civil Service over a period of time ahead of the launch of this scheme, including with the new minister in the last week.”

He added: “Our work will not be done until every wronged subpostmaster or Post Office worker is cleared without a stain on their character, and compensated fairly.”