The once-unthinkable prospect that Britain could be ripped apart this month with a vote for Scottish independence became bracingly real Monday after the campaign to keep the three-century-old union together was accused of panicking amid polls showing the referendum in a dead heat.

Just 10 days before the vote, the new surveys depicted a dramatically tightening race after months in which the “no” side appeared to hold a comfortable lead. Although both sides have questioned the accuracy of the Internet-based polls, the pro-independence camp immediately claimed the momentum.

Unionists, meanwhile, scrambled to agree on a plan for shifting power away from London and giving it to the Scottish government if the Scots choose to stay, with former prime minister Gordon Brown saying his Labor party would move aggressively to do just that.

But it was unclear whether the other major parties agreed with Labor’s plan, and the unionists were forced to spend Monday fending off accusations that they were desperate to stop a slide toward “yes.”

“They had become so overconfident. They never expected to be in this position,” said Iain Docherty, a public policy professor at the University of Glasgow. “So they’re improvising, and they may make things worse for themselves.”

Better Together supporters, who oppose the separation of Scotland, have been actively campaigning. (Jeff J. Mitchell/Getty Images)

Docherty said the unionists’ moves in the coming days are likely to be a “make-or-break moment” for the future of Scotland — and for the United Kingdom.

The potential consequences of the Sept. 18 vote are vast for a nation that could be hard-pressed to continue to call itself Britain if a third of its land mass disappears beyond a foreign border. Britain’s military, economy and politics could be reshaped with the vote — as could its image as a world power, even if that status has been long in decline.

“In terms of its impact on the British self-image, it would be analogous to the loss of empire in the 1940s, ’50s and ’60s,” said Tony Travers, a government professor at the London School of Economics.

The independence of Scotland, he said, could carry even more of a punch because Scotland has been an inextricable part of Britain’s identity for centuries. “Really, there are no parallels for it,” he said. “There’s no doubt that if the Scots vote to leave, it would be a spectacularly traumatic experience for the British political class.”

Analysts say that Scottish secession probably would bring calls for the resignation of British Prime Minister David Cameron, with less than a year to go before he is due to face voters in a general election.

The Tory leader’s main rival in that contest, Labor chief Ed Miliband, also could suffer if the vote swings to “yes”: Scotland reliably votes for Labor in the general election, and without Scottish seats in play, the Conservatives could win British elections they otherwise would lose.

Although the prospect of Scotland’s secession has been real for two years, ever since Cameron and Scottish First Minister Alex Salmond agreed on terms for a referendum, the chances seemed remote until recent days. Among the political class in London, confidence was high that the Scots would choose to stay.

But the latest surveys have abruptly shifted the mood. One, by the polling firm YouGov, showed the independence camp with a lead for the first time — albeit by an extremely narrow margin of 51 percent to 49 percent when voters who answered “don’t know” were excluded. Another survey, by Panelbase, essentially flipped those results, showing 52 percent favoring “no” and 48 percent siding with “yes.”

Both polls were based on Internet surveys, the accuracy of which has been questioned by the campaigns and by polling experts.

John Curtice, a politics professor at the University of Strathclyde, said that although the results appeared to show a shift toward “yes,” more data is needed. With turnout expected to be exceptionally high — perhaps 80 or 90 percent of Scotland’s more than 4 million eligible voters — the outcome will be unusually difficult to predict.

“The truth is that the polls have surrounded the referendum in a measure of uncertainty throughout the campaign,” Curtice said. “It may be that we’ve always been in a close race, and it’s going to continue to be close.”

The prospect of a vote for independence was already rippling through the financial markets Monday, with the pound falling to its lowest level against the dollar in nearly a year amid fears of currency confusion. British officials have said that an independent Scotland will not be permitted to use the pound; Scottish leaders say that’s a bluff.

Stock prices for Scottish-based businesses also took a hit Monday.

Independence activists say that Scotland will be better off on its own because the country’s left-leaning voters can abandon the austerity policies advanced by Britain’s Conservative-led government, and invest more in education, health and welfare.

“Scotland has all this wealth, but it’s not working for us,” said Graeme Sneddon, a young “yes” activist. “Independence offers an opportunity to redistribute that wealth.”

Sneddon said the shift in the polls reflected changes he has noticed while campaigning door to door. “We’re starting to see the surge,” he said.

But unionists were hoping Monday that the tightening polls would have the opposite effect: waking up voters to what London Mayor Boris Johnson described as a “sleepwalk to tragedy.”

“We are told that if Scotland votes to cut its ties with England, that will be a disaster on a par with the loss of the American colonies in 1776; but it is far worse than that,” Johnson wrote in an op-ed for the Daily Telegraph. “Scotland isn’t a colony, for heaven’s sake. It’s a part of our being, of what makes us ‘us.’ ”