Nicola Sturgeon’s dry sense of humour is one of her more attractive traits. So it was that when she visited Theresa May in Downing Street this week she took along a Christmas present – a bottle of Misty Isle gin. That the gin was from the Isle of Skye, the constituency of the SNP’s Westminster leader Iain Blackford, who had been dismissively told by Nicholas Soames to go back there in the Commons the day before, was entirely intentional.

There was less humour in the statement made by the First Minister outside No. 10, following the meeting. “The immigration white paper and the proposals in it represent an act of vandalism on the Scottish economy and public services,” she told waiting hacks. “Our demographics mean that we need to attract people to live and work in Scotland, and yet the proposals in this paper estimate that EU immigration will reduce by 85 per cent. That will send Scotland’s population into decline. It will depress economic growth and reduce revenues, so the impact would be devastating. It would also deprive us of talented, hard-working individuals who enrich our society.”

There are two things to say about this. First, it is vanishingly rare these days to hear a political leader set out such a positive, liberal view of immigrants and immigration. Second, there aren’t all that many people in Scotland of any political persuasion who would disagree with the First Minister’s sentiments.

There is a stark difference in the immigration narrative north and south of the border. Where the prevailing discussion at Westminster is how to better control and reduce immigration, the question at Holyrood is how to attract more of it. Here is Jackson Carlaw, currently leading the Scottish Conservatives in Ruth Davidson’s absence, speaking during a debate in Edinburgh earlier this year. I’ll quote him at a little length.

“Let me tackle directly some of the myths that are often repeated to me as an MSP—myths founded on concerns that migration alone is responsible for the pressures on our infrastructure and public services, which is simply not true.

“Yes, we have a housing shortage, but that is not because of migration. We have seen radical shifts in the way that we choose to live, with far more single home occupancy and longer life expectancy. Homes that might have been expected to appear on the open market two decades ago are now still happily occupied.

“Yes, we have busy hospitals and general practitioner surgeries, but that is not because of migration. We have a population that is living longer but is not always well. Even in the lifetime of this parliament, we have seen new issues that were not envisaged when we first met, such as dementia and diabetes arising from obesity, present enormous strategic and budgetary challenges to the national health service.

“Yes, we have busy schools, colleges and universities, but that is not because of migration. Far more of our young people stay longer at school and proceed into further education of whatever kind.

“The suggestion that migration is at the heart of the stresses in our public life and services is a fantasy, and a malicious and self-deceiving one at that. Let me be absolutely clear—I say this personally and on behalf of the Scottish Conservatives—that migration and immigration from wherever are good, necessary and desirable. There is a strong, powerful and unarguable case for migration to Scotland and we are on its side.”

Now try to imagine those words coming from the mouth of May, or Sajid Javid, or Jeremy Corbyn.

The facts make their own case. Scotland’s fertility rate is lower than every other country and region in the UK. Over the next 25 years, the number of births minus the number of deaths is projected to be negative, and so any increases in population will come from migration. The 65-74 age group is projected to increase by 17 per cent over the next 25 years, while the number of people aged 75 and above is projected to increase by 79 per cent. All other age categories will decline.

An ageing population, increasing demand on public services such as social care, the NHS and pensions, and a smaller group of working age people to pay for it all – you can see why demographics and immigration are at the forefront of the Scottish government’s mind.

This week’s white paper, as Sturgeon pointed out, has done nothing to dispel those concerns. The continued “hostile environment” embraced by the pathologically anti-immigrant May threatens to be a catastrophe for the north.

The abolition of the cap on high-skilled workers might be welcome, but the proposed £30,000 salary threshold suggests a staggering ignorance about earning potential outside London. And Scotland anyway needs access to low-skilled immigrants more than many other parts of the UK, due to its large rural economy, particularly in the tourism and agricultural sectors, and in island communities. Non-EU migration is focused in Scotland’s cities, while the countryside benefits more from EU migrants – the threat from Brexit is therefore acute.

It’s in this light that Sturgeon and her ministers are seeking a Scotland-specific solution from Whitehall. There are a number of options being knocked around, but it seems unlikely May will agree to any of them.

One is to give more time in the country to foreign students. In the 2000s, the then Labour first minister Jack McConnell introduced the Fresh Talent initiative, which allowed overseas students to stay on in Scotland for up to two years after graduation. May as Home Secretary refused to allow a reopening of that scheme - the longest a graduate can stay in the UK today is one year.

There is a suggestion that low-skilled young people from the Commonwealth and the EU could be allowed an extra year’s residency in Scotland, beyond their time in the UK, giving them longer to find a pathway to settlement.

The Scottish government currently has no formal role in the setting of immigrant quotas by the Home Office. The Migration Advisory Committee makes its recommendations to the Home Secretary each year on the list of shortage occupations, including for Scotland, but Scottish ministers can only make a submission to the process during the public evidence-gathering period, along with everyone else. This seems inarguably sub-optimal.

And there is a case – advanced by the think tank I run, Reform Scotland – that Scotland could be removed from all and any caps on immigration. Now that Holyrood has control over income tax, taxpayers north of the border have a different tax code, which would make it easier to monitor and restrict the location and movements of immigrants.

The SNP government will early next year produce a Welcome to Scotland package, aimed at showing the nation is open to immigrants regardless of the tone at Westminster. Allowing Scotland some flexibility on immigration post-Brexit will be a test of the Union’s willingness to accommodate difference. It’s a serious matter – and it’s not at all clear that May understands that.