Viewers in Scotland could be forced to pay on top of their licence fee to watch popular BBC programmes such as Doctor Who and Strictly Come Dancing, under plans for a new, post-independence Scottish public service broadcaster, Labour will warn this week.

In a recent speech to the Edinburgh International Television Festival, Alex Salmond, Scotland's First Minister, said that, as an independent nation, it was "utterly clear" there should be a new, Scottish broadcasting corporation paid for by the Scottish licence fee.

But in a debate in Westminster on Tuesday, Mr Salmond's critics will warn that hiving-off the £325m Scottish viewers contribute to the licence fee would result not just in fewer resources for the BBC south of the border but extra costs for Scots.

They suggested that, deprived of the Scottish licence fee, the BBC would have no choice but to "switch off" the signal – forcing viewers to pay for programming as they do in the Republic of Ireland. They would also be deprived of "catch-up" services such as i-player which is only free in the UK.

In Mr Salmond's speech in August he suggested that Denmark – which has a population size similar to that of Scotland might be a model. He pointed to programmes such as the The Killing and Borgen as "fantastic examples" of how quickly good-quality shows can become international hits.

Mr Salmond said Scotland would "continue to provide open access for broadcasters from the rest of the UK and elsewhere" who wished to provide entertainment and information to Scottish viewers.

But the deputy leader of the Scottish Labour Party, Anas Sarwar, said it was impossible to imagine a situation where licence fee payers in England, Wales and Northern Ireland would be asked to subsidise making BBC programmes available for free in Scotland.