A Scottish government promise to expand free childcare in the event of independence is based on economic analysis that “simply doesn’t add up”, the UK Treasury has claimed.

The Whitehall criticism of Edinburgh’s numbers on childcare is part of an attempt to undermine the credibility of the nationalist vision for independence and shore up support for the union ahead of the September 18 referendum.

The Scottish government announced in November it would offer 30 hours of childcare a week for children over the age of one in the event of independence. It said this could lead to a 6 percentage point increase in female participation in the labour force – about 104,000 extra women in work – which would boost the economy and lift tax revenues by £700m.

But according to the Treasury, Office for National Statistics data suggests 61 per cent of mothers in the UK with children under three are already in work. The Treasury said that even if every one of the estimated 83,000 non-working mothers who could benefit from the policy entered the workforce, the Scottish government’s estimate would still be 21,000 people too high.

“Their costing is worse than just wishful thinking, the sums don’t work,” a Treasury official said in a briefing on Friday.

Chief Secretary to the Treasury Danny Alexander said: “This is typical of the nationalist elite who think they can con voters by inventing mothers that don’t exist and then assume that they will all get back into work. They will say anything, no matter how far-fetched to get their way.”

The Treasury forecasts the policy would increase the female labour force participation by 0.6 percentage points and boost tax revenues by about £130m per year.

An aide to John Swinney, Scotland’s finance secretary, said the Treasury’s attack was “deeply flawed”.

“In terms of our childcare commitments and boosting the number of women in work, it is our commitment to stop wasting money on Trident and on contributing to the running costs of Westminster that gives us the ability to invest in these other priorities,” he said.

Better childcare was one of the few flagship post-independence policies set out in detail last year in the Scottish government’s “white paper” on a future outside the UK.

The Treasury plans to release a paper of its own on Wednesday that aims to put a “price tag” on the impact of independence on Scotland’s fiscal position.

The paper, which officials have been working on for months, is the latest in a series of reports by the UK ministries intended to make the case that Scotland would be worse off if it votes for independence.

The paper will argue that Scotland’s fiscal position will be worse than the UK’s from “day one” of independence. The Scottish government forecasts its deficit would be 3.2 per cent of gross domestic product in 2016/17. But other independent estimates from the Institute for Fiscal Studies and Citigroup suggest Scotland’s deficit will be between 5.2 and 5.5 per cent of GDP.

Those differences are explained in large part by disagreements about how much North Sea oil and gas can be expected to swell the Scottish government’s coffers.

The Treasury paper will point out that even the Scottish government’s most pessimistic forecast for oil revenues is about £4bn higher than the forecast from the Office for Budget Responsibility, the UK’s official fiscal watchdog.

The Treasury report will also argue that Scotland would suffer from worse demographics than the UK as a whole. In order to keep the ratio of pensioners to working-age people in line with the UK’s, Scotland would need to encourage net immigration of about 24,000 a year, the Treasury said. That would mean adding the equivalent of the population of Edinburgh over 20 years.

Immigrants in Scotland make up about 7 per cent of the population, half the level in England, and opinion polls suggest more tolerance for increased flows north of the border. Scotland is less densely populated than England.

A 2011 Ipsos Mori poll for the Oxford Migration Observatory found 20 per cent of Scots would support the number of immigrants being increased by “a lot”, compared with just 2.6 per cent in the south of England.

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