IN the private polling and focus group conversations which inform campaign strategists about how to approach the referendum debate, the health service consistently crops up as one of the most important issues for people as they consider how to cast their vote.

On the face of it, that makes no sense at all. Health is wholly devolved. Since 1999, decisions on NHS Scotland's budget and how it is run have been taken in Edinburgh. The referendum is about whether other things - economic policy, foreign affairs, defence and so on - should also be decided in Scotland.

That has not, however, stopped Alex Salmond from putting the fate of Scotland's NHS at the heart of his independence campaign. Doubtless mindful of the focus group feedback, the SNP has mounted a major effort to persuade people that the health service it runs is under threat from Westminster. The danger, it says, lies in the growing privatisation of healthcare south of the Border.

It began in earnest last week when Dr Philippa Whitford, a consultant breast surgeon at Crosshouse Hospital in Kilmarnock, claimed England's NHS will be gone in five years and Scotland's would wither away within a decade unless there was a Yes vote. She suggested privatisation by the back door would be inevitable. Writing in The Herald, another doctor, Glasgow GP and NHS for Yes campaigner Anne Mullin, said devolution could not protect the NHS from the "great, big sell-off" down south.

Deputy First Minister Nicola Sturgeon picked up the theme, warning privatisation down south would lead to "hugely damaging cuts" to Scotland's health service through the knock-on effect of the Barnett Formula, used to allocate public funding around the UK. "People should be under no illusion about the threat to the NHS here in Scotland from Westminster's privatisation agenda," she warned.

Mr Salmond made the same point in a speech in Liverpool. "Under the Westminster system," he said, "cuts to spending in England automatically trigger cuts in Scotland."

How credible is the threat to Scotland's NHS? There is no doubting the scale of privatisation in the English NHS. Under the Health and Social Care Act, healthcare provision was opened up to private companies and third-sector organisations. Since the Act came into force last year, more than half of all contracts in England, worth billions of pounds, have gone to private providers. But companies are being paid by the NHS: privatisation does not automatically mean cuts in health spending.

Fans of privatisation might argue that the process will improve efficiency and allow costs to be cut in the long run, but Mr Salmond rejects that analysis, insisting during his Liverpool visit that Scotland's publicly-run NHS is more efficient. It's hard to imagine David Cameron or Ed Miliband fighting next year's General Election promising to cut health spending.

Indeed, it is reported that Labour is considering a 1 per cent hike in National Insurance to boost the NHS budget. Mr Cameron came to power in 2010 promising to protect the NHS budget and has just achieved it. It may be the smallest increase for half a century but, between 2011/12 and 2014/15 NHS England's budget is set to rise by 0.1 per cent in real terms.

The Tories believe privatisation is more efficient but their rationale is to make the public pound stretch further, not spend fewer pounds. As in Scotland, the English NHS is under immense pressure to meet ever-growing demand with barely-rising budgets. Health chiefs across Britain have been ordered to make savings not so money can be diverted into schools or roads, but to maintain frontline services.

The SNP may explain the link between reforms in England and cuts in Scotland in greater detail in the weeks ahead. In the meantime, the No campaign accuses Mr Salmond of scaremongering. As health unexpectedly takes centre stage in the referendum debate, Better Together claims an independent Scotland's finances would not be strong enough to maintain spending at present levels without recourse to tax rises. No prizes for guessing the Yes campaign's response: scaremongering.