The future of the health service is set to be the key battleground in the Scottish independence campaign this week, with polls suggesting that the lead for the no camp is narrowing and the prospect of NHS cuts in Scotland is pushing support for independence among women over the crucial 50% mark.

Despite evidence that voters remain unconvinced by Alex Salmond's currency plans, which have come under sustained scrutiny following his bruising television encounter with Alistair Darling two weeks ago, an ICM poll for Scotland on Sunday found that support for independence had risen by four percentage points since last month to 38%, as more undecided voters make up their minds with a month to go to the referendum.

Excluding undecided voters, the poll found the lead for no remained decisive at 55%, a decrease of two points from last month, while support for yes had increased by two points to 45%.

On Monday, Salmond will continue his attempt to shift the focus on to the health service in what is being described as a new Declaration of Arbroath. Speaking before a meeting of the Scottish cabinet in the town where the historic declaration of Scottish independence was made in 1320, he will state that a yes vote would "protect our publicly owned, publicly run NHS forever from Westminster privatisation and cuts".

Last week, the first minister offered to enshrine a free NHS in a written constitution after independence, and claimed that a yes vote was needed to prevent increasing privatisation and internal NHS competition in England from spilling over into Scotland. The opposition accused him of spreading "the biggest lie of the independence campaign".

The Scottish Conservative health spokesman, Jackson Carlaw, said the suggestion that a no vote was a threat to healthcare was "shameless scaremongering", pointing to figures that showed spending on private healthcare by the NHS in Scotland at a five-year high.

"For all the SNP's tall talk on private healthcare, they have spent more than £400m on the sector since coming to power," he said. "The fact is the health service in Scotland is completely devolved, and SNP claims that a no vote threatens its existence are nothing but shameless scaremongering."

Dr Philippa Whitford, a member of Women for Independence and a consultant breast surgeon, welcomed the results of a Panelbase poll commissioned by Yes Scotland, in which 52% of women said they were more likely to vote for independence if the increased role of the private sector in the NHS in England were to have an adverse effect on the Scottish budget.

"No one is now attempting to deny that the NHS in England is being privatised, as 70% of all new NHS contracts have gone to private firms in the last year," Whitford said. "Patients in England still pay prescription charges of more than £8 per item, and payments of £10-£25 to see a GP have been suggested by some thinktanks to cope with NHS debt. A recent survey reported that almost 50% of leaders in NHS England believe that charges are inevitable within 10 years, which would also lead to a reduction in our funding.

"The main threat is simply that Westminster sets the total Scottish budget and we face a £2bn share of the £25bn austerity cuts already announced by George Osborne."