The British establishment is still lying down in a darkened room after its brush with constitutional mortality, and so Nicola Sturgeon is being a good neighbour: the curtains are still closed, there are no jerky movements and she has asked nurse to come along soon and mop some more brows. There is certainly no loud talk of, you know, another referendum. Well certainly not now, at any rate. But its whispered presence lingers still.

In two weeks' time, Sturgeon will become leader of the Scottish National party and the first female first minister of Scotland. Last Wednesday she announced her intention to succeed her boss Alex Salmond who, in the wake of seeing the death of his dream of leading Scotland to independence, stepped down after more than 20 years at the helm of the party, seven of them as first minister.

For now, Sturgeon has expressed her commitment to ensuring that the Smith Commission to deliver more devolved powers to Scotland will work, and that the SNP will participate in it fully. But accompanying the reassuring words of co-operation and compromise there is an implicit warning that the West- minster establishment had better deliver on its promise of significantly increased devolved powers to Holyrood or a heavy toll will be exacted by the Scottish public.

About 1.6 million of them voted yes – 45% of a massive turnout – and since the result was announced just over a week ago SNP membership has risen from about 25,000 to approaching 70,000.

"In the final days of the campaign, the unionist parties made a solemn promise, styled as a vow, to the people of Scotland," she says. "The language used around that was of devo max or something close to federalism or home rule. This took it beyond the detail of what these parties had previously offered. This was something that was going to markedly change the ability of the Scottish parliament to deliver on the economy and on welfare. And so this is what now needs to be defined and delivered. This is where people are in their expectations.

"Accepting the result means more than just accepting that yes didn't win. It means accepting that there was a very strong demand for change in that vote. We're going into this process genuinely, and as active participants; we're not going in to see it fail. We want to help make it a success. But people are not going to be easily bought off by a few more powers in a list that allows the Westminster parties merely to tick some boxes."

Sturgeon is convinced that the extraordinary move by the leaders of the three main unionist parties was a game-changing moment in the referendum campaign. It came after a breakthrough poll showed the yes vote ahead by two points and thus indicated that threats over a currency union had not had any real effect on the contest. "A pivotal point was the pledge to deliver more powers that they all signed. It gave people who had maybe been sympathetic to independence but had been concerned about perceived risks a reason to vote no in the expectation that there would be meaningful change. So this is what the unionist parties must deliver," she says.

"I accept, though, that we won't get everything we want out of that process and that there will have to be compromise. But the other parties are going to have to compromise as well. It's not just any list of new powers that is important but the ability for them to interact with each other as a package and in the context of the Scottish parliament."

Would she not accept that Holyrood already has significant tax-varying powers which the SNP had chosen not to deploy? "The tax-raising powers we have are merely to raise or lower the basic rate of income tax by 3p. The risk we would run in deploying this in isolation would be to hit those people at the lower end of the income spectrum, the very people we're trying to help. The more restrictive the tax powers are the more difficult it is to use them to help people and be more socially progressive. What we need is the panoply of tax powers to ensure that the levers we're pulling are having the desired effect."

Events, however, may propel Scotland towards another referendum sooner rather than later without any nudge from the SNP. If Westminster substantively reneged on the spirit of the Gordon Brown pledge, under pressure from Ukip-threatened fragile Tories, then this would lead to "a very, very angry reaction in Scotland", according to Sturgeon. And if that were then followed by a yes vote to leave the European Union while Scots voted no, then wouldn't there in effect be a responsibility to include another referendum on the manifesto for Holyrood elections in 2016?

"There might be calls, and not just from within the party. However, I'm not planning for a referendum as I don't think there is an appetite for it right now. But if we get to a situation where Westminster has manifestly failed to deliver on its promises then there'll be anger. They have to understand they themselves raised expectations in terms of the pledge. Circumstances and not politicians dictate when and whether you have referendums."

In the days following the referendum result there have been strange signs and portents that leave you wondering if the normal laws of politics still apply. For the avoidance of doubt, the noes won by 10 clear points, and while there may have been scaremongering by the four horsemen of the British apocalypse, to suggest that Scots were cowed into no is condescending in the extreme. Yet Labour, on the victorious side, is facing a bleak future in Scotland, while the SNP, on the losing side, has seen a jump in membership at a rate unprecedented in modern UK electoral history.

"My personal inbox is full of messages from people who have said, 'I've always voted Labour but I'm never doing so again as long as I live'; how indicative that is I don't yet know," says Sturgeon. "This feels like a watershed moment for Labour in Scotland. In this city [Glasgow], they saw the wholesale desertion of their own core support.

"They campaigned with the Tories to perpetuate a situation where we are at the mercy of Tory governments. People remember how many times the country had voted Labour only to get the Tories.

"If people wake up on the morning after a general election only to find we have another Tory government again then that anger is only going to intensify."