A separate Scottish visa system would “increase complexity and create frictions when workers move locations”, a Home Office minister told the Commons.

Seema Malhotra made the comments a week after the UK Government slapped down John Grady, the Labour MP for Glasgow East, who appeared to suggest the UK Government was considering a Scottish such a scheme.

Some business organisations were disappointed the proposal was not "on the table" after calling for  the Labour Government to consider one to help address a shortage of staff in certain areas including in hospitality and the care sector.

Following last week's row SNP MP Pete Wishart (Perth and Kinross-shire) asked Ms Malhotra today what discussions she has had with the Scottish Government on the potential merits of devolving the power to introduce a Scottish visa scheme.

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“We are not introducing a Scottish visa scheme, or devolving control with immigration policy, and this has been made clear to the Scottish Government," she told MPs.

“Instead, we must together address the underlying causes of skills shortages, and overseas recruitment in different parts of the UK, which this Government is doing.”

Mr Wishart responded: “I thank the minister for her tiresome and repetitive response, she will know that Scotland has a whole range of demographic and population difficulties that need urgently addressed.

“Every sector, from social care to hospitality, including business leaders, are calling out for drastic actions. Even her Scottish Labour colleagues are beginning to understand the enormity of this task.”

He added: “Instead of slapping down her Scottish colleagues, and instead of rejecting this out of hand, why doesn’t she work with us just to see if it might actually work?”

Ms Malhotra replied: “ "Net migration must come down, which trebled under the last government, largely driven by overseas recruitment. Immigration is a reserved matter, working in the interest of the whole of the UK and previous schemes along the lines he has suggested has only succeeded in restricting movement and rights in creating internal UK borders adding different roles for different locations would also increase complexity and create frictions when workers move locations." 

Leon Thompson, the executive director of UKHospitality Scotland, told The Herald last week he was "very disappointed" when he read the policy was not being pursued.

"The hospitality and tourism industry across Scotland have been calling for a Scotland visa for some time," he said.

"We believe it is really one of the ways in which we can help address the skills and workforce shortage that we have in the industry, particularly but not exclusively in rural areas where we have depopulation and declining population of working age which is making it incredibly difficult for businesses to operate to optimal level.

"They just cannot get the workers and the people with the skills to offer the service our guests and visitors are looking for.

He added: "There needs to be some further conversations at how we have arrived at a situation where it is not being considered at all when it was part of the conversation before the election. Nobody expected anything like this to happen quickly but to see it taken off the table altogether will be a blow to the sector."

Speaking today, Labour MP Chris Murra told the Commons: "Scotland is a diverse place. Some areas are seeing depopulation, but areas like East Lothian, which I represent, are seeing unprecedented population growth.

"Will the minister commit to working constructively with the Scottish Government on their woeful population strategy which has comprehensively failed to address Scotland's demographic challenges."

Ms Malhotra said: "We are committed to working with the Scottish Government on this and all issues, and indeed, many of the levers to address depopulation in Scotland are through powers the Scottish government already has at its disposal.

"Indeed, the reasons for local workers leaving particular areas must be addressed through investment in jobs in infrastructure and public services. Many of these issues that we must tackle also together."