There can be no excuses for complacency or ignorance, with polls suggesting an independent Scotland is only 10 days away

With only 10 days to go, the rest of Britain finally awoke on Sunday to the scale and importance of what is happening in Scotland. For years, the rise of Scottish national feeling has been underestimated and misunderstood. The possibility that the United Kingdom might be heading for the history books has been complacently dismissed as unthinkable. But there can be no excuse for any ignorance or complacency now.

This weekend the unthinkable has elbowed its way into the driving seat of the Scottish campaign. No other issue now matters in British politics. These may not be 10 days that will shake the world, as John Reed called the Russian revolution. But they will be 10 days that could change all our lives, shaking the British state and its people to their very foundations.

YouGov's opinion poll for the Sunday Times revealed a nation parked on a cliff edge, with the yes campaign enjoying a 51%-49% lead. In all the long months and years of the argument about Scotland's future, such a thing has never, ever happened before — until now a yes lead was not even close. But the message was simple and electrifying. An independent Scotland is 10 days away.

Sunday's poll has been coming. The trend in the polls has been slowly narrowing all year, slowly at first, followed by a long pause, then slowly once more. In the last two weeks, however, the long-held advantage for the pro-union camp has suddenly withered away.

Clearly something went snap in a lot of Scots' minds after Alex Salmond outpunched Alistair Darling in their second televised debate, just two weeks ago. YouGov's detailed figures suggest that it went snap among Labour voters in particular. But other groups have shifted allegiance too.

Four weeks ago, only 18% of Labour voters were in the yes camp. Now fully 35% say they will reject their party's campaign against separation and will vote yes to independence. Four weeks ago, only 33% of women were committed to yes. Now 47%, nearly half of Scottish women, are saying yes. Working-class support for independence has risen from 41% to 56%. And support among under-40s has leapt from 39% to 60%.

If these figures hold, they suggest that Salmond has now won the key battle of the peaceful war. The battle to shake the Labour vote, particularly in the west of Scotland, has long been seen as the key to the outcome on 18 September. But will Salmond's success hold up as the campaign reaches white heat over the next 10 days?

There are good cases to be made on both sides of that argument. For the yes campaign, the big positives are momentum and confidence. Sunday's poll is likely to be echoed by others. The belief that this is really winnable is the best recruiting sergeant that Salmond could have hoped for. With the well-honed professionalism of the SNP ground campaign, the message that it is safe to vote yes will be driven home every hour of every day from now to polling day.

On the other hand, YouGov's poll isn't the final result. Its findings are within the margin of error. Sunday's other, much less widely reported poll, from Panelbase, shows the no campaign still in the lead by 52% to 48%. That is still close and it is within the margin of error too. But it deserves attention because Panelbase's previous surveys have tended to be more favourable to the yes campaign than those conducted by other polling companies, including YouGov.

It is also possible that YouGov's poll will be such a shock that it changes the game. There was talk yesterday of a big new constitutional offer to try to keep the Scots in the Union, though it feels perilously late for that. Some voters may be alarmed by the poll's in-your-face evidence that a yes vote really could happen. Others, by contrast, may feel emboldened. That's why the next 10 days are such a cliff-hanger.

Those who want to save the union will draw some comfort from the turnaround that took place in the final hours of the Quebec independence referendum in 1995. With five days to go before the Quebec vote, the yes campaign was six points up. Three days before the vote, an estimated 100,000 Canadians, mostly from outside Quebec, travelled to Montreal for a "unity rally" to plead with the voters to stay in Canada. On polling day, with a 93% turnout, Quebec narrowly voted 50.5% to 49.5% to remain a Canadian province. If just over 27,000 voters had changed their minds, Quebec would be an independent state today.

In Scotland, slightly smaller than Quebec, even fewer voters may hold the final key. But where is the unity rally to love-bomb the Scots to stay? English opinion is overwhelmingly in favour of Scots remaining in the UK. Do the English care enough, or know how to get their message across?

Scotland's swing voters certainly will have no place to hide over the next 10 days. For they hold the future not just of Scotland in their hands, but the future of Britain too.

• This article was amended on 9 September 2014 to change the term "enormity" to "scale and importance" in the first paragraph.