John Swinney would work with Starmer on relaxing immigration rules for Scotland

There are now more than a million people aged over 65 in Scotland, with the total growing by 22.3 per cent since 2011. In comparison, the number of under-14s has dropped by 2.5 per cent over the same period and the total aged between 15 and 64 has fallen 1.1 per cent.

Dame Jackie told the Herald on Sunday that Labour would introduce a new system that matched immigration to a new system that tackled skill shortages and encouraged more UK immigrants to move to Scotland.

“So we would do what the Tories have not done, which is to marry those two together because I know there are skill shortages in different parts of the UK including in Scotland – for instance in the care sector,” she said.

“So how do we make sure to match our immigration system to skills is something that is very firmly on the agenda at a UK level and Scotland would benefit from that.”

She added: “Given the levels of immigration that there are – and that’s become a hot topic – actually not many people are ending up in Scotland and we need to understand why that is and whether there is something we can do to incentivise people to come more to Scotland once they have reached the UK, that is a job for us to think through.”

Pressed if Labour would be open to some devolution of immigration powers, including a Scottish visa, she said: “There would be discussions to have at that time until then I am absolutely fixed on July 4 polling day.

“All my energy is going into that. But I would expect governments to work together, to talk to each other, to respond to each other’s needs.”

Mr Swinney told BBC Scotland’s Sunday Show that talks with Labour had not started but “I welcome” Dame Jackie’s intervention.

“Because if it’s an indication of some of the practical steps that might come from inter-governmental relations with an incoming Labour government, then nobody will engage in that more strongly than me,” he said.

However, he said he was a “wee bit doubtful” whether this would transpire given Labour’s pledges to clamp down on immigration “on every UK television channel”, saying it had taken a “very, very hostile attitude.”