The Bill to exonerate victims of the Post Office Horizon scandal in Scotland has completed its second parliamentary hurdle, with those who have lost an appeal against their conviction set to be included.

But the Post Office (Horizon System) Offences (Scotland) Bill will now be put on hold until the UK-wide legislation is passed to ensure subpostmasters and subpostmistresses north of the border are able to access the redress scheme.

MSPs voted to treat the Bill as emergency legislation earlier this month, expediting its passage and meaning stage two would be done before all MSPs in the Holyrood chamber as opposed to by a committee.

In a largely consensual debate, one of the key changes to the legislation will see the Bill include those who have lost an appeal against their conviction.

Justice Secretary Angela Constance said: “We know now that in many appeal cases, members of the judiciary would not be aware of the Horizon system issues at the time of appeal decisions.

“And even if an appeal was considered after the problems with Horizon were known about, any convictions considered on appeal would have been subject to a different test than convictions that are quashed by this Bill.

“These amendments will ensure that every person whose conviction meets the criteria of the Bill will be treated equally and will have their convictions quashed, regardless of previous appeal decisions.”

Ms Constance said she has sought assurances from UK minister Kevin Hollinrake that the change will not impact on the access of victims to the redress scheme.

“The assurance that I received cleared the way for me to lodge these amendments and ensure that postmasters who previously sought to appeal their convictions are not treated less favourably than their peers,” she said.

Speaking later on Thursday, the Justice Secretary said the passage of the UK-wide Bill expected next week – brought forward by the imminent dissolution of parliament ahead of the General Election – will allow Holyrood to plan for the third and final stage of the Bill to take place “as soon as possible”.

“We are also committed to seeking expedited Royal Assent so victims of this terrible miscarriage of justice can finally have their names cleared and access UK Government compensation schemes,” she added.