Humza Yousaf said he has received a “positive” response from Rishi Sunak on the Post Office Horizon scandal, pledging the UK and Scottish governments will work quickly to overturn wrongful convictions.

Scotland’s First Minister said legislation overturning the convictions will be applied on a UK-wide basis, after receiving a response to his letter to the Prime Minister.

Mr Yousaf said the easiest way to do this is through a legislative consent motion, where Holyrood allows Westminster to pass a law affecting a devolved area.

It comes after Scotland’s top prosecutor, the Lord Advocate, apologised to those who were wrongly prosecuted.

Unlike south of the border, prosecutions in Scotland were undertaken by the Crown Office using evidence from the Post Office as a reporting agency.

Lord Advocate Dorothy Bain KC said in a statement at Holyrood on Tuesday that the Crown Office had been repeatedly misled and 54 people may have been wrongfully convicted in Scotland.

The First Minister spoke to journalists on Wednesday during a visit to South Lanarkshire.

He said: “There’s a positive response from the Prime Minister and of course, our officials and ministers are engaging as we speak.”

He said Scotland’s Justice Secretary is engaging with her counterparts around the UK, adding: “What I think the easiest option would be would probably be for a legislative consent motion to be adopted by the Scottish Parliament to allow that legislation to apply on a UK-wide basis.

“We’re not quite at that stage yet, but we are looking to work at pace.”

He said the mass overturning of wrongful convictions is still an option and would be the quickest way of dealing with the scandal, saying people have been waiting “far too long for justice”.

Mr Yousaf said the Prime Minister’s response had emphasised the need for urgency, adding: “For all the differences I have often got with the UK Government, I have to say on this one they certainly seem willing to work with the Scottish Government and work at pace.”