The BBC says it must maintain its impartiality and will not comment on any issue which might sway the vote

The BBC is under political pressure to reveal details of a highly charged internal study which found that viewers in an independent Scotland would have to pay almost double their current licence fee if they wanted to continue watching and listening to the same BBC shows.

Labour's former culture secretary Ben Bradshaw has called on the corporation to publish the figures "immediately so people in Scotland have the facts before they vote".

According to sources with close knowledge of the matter, a BBC paper drawn up three years ago compared the total amount Scottish viewers paid towards the licence fee with the value of the services they received from the corporation. It is understood that the figures – one source said the internal paper concluded that the value the Scottish audience receive is "well north … almost double" the total revenue raised by their collective licence fees – were seen by some of the most senior BBC executives under the tenure of the then director general, Mark Thompson.

One source said the findings were shocking as the study found Scottish viewers received "way above" the value of BBC services compared with the amount of licence fees they paid. Another said: "In Scotland, revenue raised is well south of the value of services they receive."

Currently around £350m is raised from the 2.4m households in Scotland. The costs of running the BBC's services in Scotland are part of a complex internal financial structure, partly because they are intermingled with those for other countries, such as BBC Wales.

Sources say that one of the most expensive elements is the transmission of radio and television programmes in Scotland due to its more widely dispersed population and topography. BBC Radio Scotland costs £32.2m – almost double the amount BBC Radio Wales does, for example.

One insider explained why the figures had not been released: "The mood within the BBC then and now is that the corporation cannot get involved in anything that would sway the vote."

BBC executives, including another Labour former culture secretary, James Purnell, who is now the corporation's director of strategy and digital, have stressed how important it is for the BBC to be seen to be independent in its reporting of the referendum.

This view was repeated by the incoming chair of the BBC Trust, Rona Fairhead, during her appearance in front of MPs earlier this week.At the hearing, Bradshaw asked Fairhead what contingency plans the BBC had made for an independent Scotland, and how much the licence fee would have to increase. She replied that no planning would be done until after the referendum.

"The BBC will focus on impartial and well-informed coverage," she said. "The people of Scotland will be given all the information to make their decision … The most important thing is that impartiality can't be seen to be questioned."

Bradshaw told the Guardian it was essential that the BBC published the figures.

"The future of the BBC in Scotland and the level of the licence fee was raised with me on the doorstep when I was campaigning in Scotland this week," he said. "That is why I raised it with the incoming BBC chair. In Denmark, which has a similar population to Scotland, the licence fee is more than double the UK's.

If Scots wish to keep a Scottish BBC or something like it in the event of independence they will lose the BBC's economy of scale and will face paying much more if they wish to keep quality public service broadcasting."

The BBC did not deny that the figures existed but a spokesman said: "To suggest there's some sort of explosive report dating back three years is nonsense. The BBC regularly carries out a wide range of analyses looking at various issues, and of course we look at distribution and other costs across the UK.

"Last year we published a comprehensive set of facts and figures about the BBC in Scotland and made it clear we would not be entering into any public or private discussions about the future or the shape and nature of BBC services after the referendum until that referendum has taken place."

He added: "Our focus is on providing the highest quality, most impartial and balanced coverage so audiences have access to the information they need."

• This article was amended on 12 September 2014 to remove a reference to the BBC paper suggesting that in an independent Scotland, the annual BBC licence fee would have be raised to almost £300 per household. The Guardian understands the paper concluded that the value of BBC services to the Scottish audience is almost double the money raised by their licence fees, but accepts the BBC's statement that it has not done any calculations about the level of the licence fee post-independence