Yvette Cooper, the shadow home secretary, has called for an "open, honest debate" about Alex Salmond's plans to loosen Scottish immigration controls after independence.

Cooper said the first minister's plans for Scotland to pursue a more liberal immigration policy raised questions about the impact increased rates of migration would have on public services, wages and on the rest of the UK.

She told the Guardian that Salmond needed to publish the Scottish government's analysis about the numbers of additional migrants and the potential costs and benefits to the economy, particularly to meet a predicted pensions deficit because of Scotland's ageing population.

"There are issues around jobs, the affordability of public services and the affordability of pensions," she said before speaking at an anti-independence rally by Better Together in Inverness. "These things are incredibly important for the future of Scotland."

Salmond's government had to be far more transparent about its evidence but it remained unclear whether the Scottish government had done any analysis of those costs, she said.

She insisted Labour's concerns were based on an independent Scotland's need for higher immigration simply to offset the larger and growing gap in Scotland between working age adults and pensioners. But the last Labour government made mistakes by failing to cap eastern European migration, she added.

"It would be irresponsible of them not to have done that analysis," Cooper said. "We have to have a sensible, honest debate about immigration. We do not have to have a divisive, shrill debate."

The tougher stance by the UK parties on immigration policy, influenced by the surge in support for Ukip in many parts of England, has been attacked repeatedly by Scottish ministers and pro-independence groups in the referendum as proof of a rightward drift in English politics, to attract centre-left voters to a yes vote.

That suggests that taking a tougher stance on immigration is a risky strategy for Labour in the independence debate, just as Ed Miliband hosts a full shadow cabinet meeting in Glasgow on Fridayand as polls suggest the pro-UK campaign is ailing, with support for independence climbing.

Better Together strategists believe that, excluding political activists, voters' views on immigration are close to the UK average.

A recent British Social Attitudes survey shows 69% of Scots want immigration reduced, compared with 77% of UK voters overall. Although more Scots think migrants are good for a country's cultural life, only 2% of Scottish voters want immigration increased, the BSA found.

The Scottish government white paper pledges a more liberal approach. It would lower the wage and wealth thresholds to suit Scottish needs, target immigration at particular industries and depopulated rural areas, reinstate post-study work visas and have a "more humane" asylum policy.

Accusing the UK government of aggressive attacks on asylum seekers, it would pursue a much more "humane" asylum policy after independence. But the Scottish government admitted that greater migration was needed to boost Scotland's working age population, which is ageing more quickly than the UK average.

The UK government, backed by former Labour prime minister Gordon Brown, has argued this week that an independent Scotland would in truth need much greater immigration to help fill a significant black hole in the affordability of pensions because of the ageing population.

Cooper said that required many more lower skilled workers entering Scotland. One estimate suggests up to 1 million more migrants would be needed by 2051, to meet the higher costs of that ageing population.

UK government ministers have already warned that they would not allow a Scotland with markedly different immigration policies to join the common travel area that the UK and Ireland share because that relies on closely-aligned immigration rules. That would mean border controls after independence and force Scotland to join the EU's Schengen agreement.

Asked about Labour's stance on this, Cooper said: "I'm not going to speculate on different scenarios. What nobody wants is border controls at Berwick-upon-Tweed. But we would need to be conscious about what the impact of different immigration policies would be. Different immigration policies have consequences for border controls."

Christian Allard, a French-born SNP MSP, said: "The reality is that pensions are more affordable in Scotland than in the rest of the UK, a view supported by the National Institute of Economic and Social Research, who have also made clear that the demographic challenge is no more significant for Scotland than it is to the rest of the UK.

"Yvette Cooper's rhetoric on immigration is also deeply worrying and yet another example of how Ukip is dictating Westminster's agenda – despite the party being completely irrelevant in Scotland."