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Aye or naw? UK PM pleads with Scottish to stay

U.K. Prime Minister David Cameron has issued a plaintive lament worthy of a Scottish dirge as the British government escalates its campaign to keep Scotland part of the U.K.

"We matter more in the world together," Cameron said in a speech on Friday, ahead of a referendum on Scottish independence in September which could end more than three centuries of Scotland as part of the U.K. The loss of Scotland would "deeply diminish" the U.K., he argued.

(Read more: Scotland independence:Widnae it work?)

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But will Cameron's plea be enough to woo the third of Scots who have yet to make up their mind on independence?

Cameron, an Old Etonian and the son of a millionaire, is perceived as out of touch and upper class in Scotland, where his Conservative Party has only one member of parliament.

In contrast, Alex Salmond, the leader of the Scottish National Party who has spearheaded the referendum campaign, is a popular figure whose party won the most Scottish votes in the last election.

(Read more: Carney to Scotland: Be careful what you wish for)

Wary of interfering too closely, the British government has until now been content to let Alistair Darling, former Chancellor of the Exchequer under the last Labour government, lead the campaign against the referendum.

Yet there are concerns that the "No" campaign has not been rousing enough after a recent poll, conducted by researcher, revealed that the "Yes" campaign had gained ground.

David Cameron's message to Scotland
David Cameron's message to Scotland

What is common across all the polls, however, is the large number of undecided voters – which consistently make up between one quarter and one third of those surveyed.

In recent weeks, the British government has attempted to sway these voters by warning about the potentially dire effects of independence on the Scottish economy. Governor of the Bank of England Mark Carney, Bob Dudley, BP's chief executive, and a variety of business groups are among those that have highlighted the possible economic issues.

"Many businesses are now setting out their concerns, putting their heads above the parapet and saying why they are opposed to an independent Scotland," Terry Scuoler, chief executive of manufacturers' body EEF, and a native of Glasgow, said following Cameron's speech.

(Read more: Salmond digs in on pound and Scottish taxes)

"Many others are telling me privately that they are against any suggestion of Scotland ejecting itself from the U.K. The enemy of investment and stability in business is uncertainty. While the economic risks around independence are not fully quantified, they do represent a significant gamble."

The "No" campaign argues that Scotland's currency, European Union membership, industry and even banks would be threatened if it was to pull away from the rest of the U.K.

BoE's Carney on Scotland-UK currency union
BoE's Carney on Scotland-UK currency union

Assets held by Scotland's banks, including bailed-out Royal Bank of Scotland, are worth more than twelve times its gross domestic product (GDP). This is a much larger multiple than that of Iceland's in 2007, for example, just before its 2008 banking collapse.

Scotland's departure from the U.K. could also threaten the country's international standing, shrink its army and even have consequences for its nuclear deterrent – many of the U.K.'s Trident nuclear missiles are currently located in Scotland.

And there are concerns that, if Scotland becomes independent, the question of Northern Ireland's independence could rear its head.

(Read more: Ukraine for Russia, just like Scotland for UK: VTB Bank CEO)

The "Yes" campaign, however, say that an independent Scotland could control the North Sea oil revenues. It also argues that left-leaning Scotland fares less well when a right-wing party like Cameron's Conservatives, which has embarked on cost-cutting reforms to the benefits, legal and healthcare system, holds power in London.

Rupert Murdoch, the News Corp media tycoon who has Scottish ancestry, has backed the "Yes" campaign in the past on Twitter, but the Scottish Sun, his main newspaper interest in the country, has not sided with either the "ayes" or "naws" so far. Other businessmen closer to home back the campaign under the umbrella of the Business for Scotland group, which says it has over 1,300 members.

"While David Cameron is focused on narrow arguments of national identity, substantial economic evidence has confirmed that Scotland will be a wealthy independent nation," Gordon MacIntyre-Kemp, chief executive of Business for Scotland, said.

"With such a strong fiscal position, combined with our natural resources and the resurgence of Scotland's entrepreneurial spirit, independence is the business opportunity of a lifetime."

- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.