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Most successful politicians have a nickname they probably wouldn’t choose but which clings to them like reputational superglue. In the case of Nicola Sturgeon, Scotland’s First Minister, it’s the “nippy sweetie” — an insistent talkative female. It sounds like a troublesome tag to cart around in mid-life (she’s a young-looking 44). Gamely, she insists it was meant as a compliment for her stalwart defence of jobs at Govan’s shipyard. Only a Scot could have come up with that soubriquet and called it well-meant.

It’s not the first time that Sturgeon has turned a somewhat dour reputation as a Robo-Nat to advantage. She failed twice to get elected to Westminster in the 1990s — “I had a lucky escape,” she says — and ran for the leadership of the Scottish National Party in 2004, but withdrew in favour of Alex Salmond. When he resigned after the narrowly lost referendum in September, she finally seized the helm of the party she joined as a 16-year-old.

On an official sashay to London to pick up reform hints from improved London schools, she’s sitting in the glass-and-steel splendour of Aberdeen Asset Management’s offices in the City: a well- groomed figure, surrounded by female aides. A helmet of hair once unkindly compared by a writer on The Scotsman to “Rod Stewart in his early mod pomp”, has transformed to a swishy, golden-brown bob, sprayed firmly into place.

A plum jacket, saucy shoes and hefty make up are part of the new Sturgeon look? She concedes an interest in high heels, though she insists that “David Cameron wears as much make-up as I do”.

Her makeover has coincided with a great leap forward for a party which has moved from the fringes of the national debate to the spotlight of the May election. If you’re a “Better Together” believer in keeping the Scots in the United Kingdom, you might consider the story ended with the relief of a narrow win for the “Nos” and a sigh of relief from unionists ranging from David Bowie to Her Majesty.

For Sturgeon and her allies, it was a near-miss that shook the London Establishment. “It was a success,” she insists, although she does admit it was “less of a success than we would have liked”. But her party has the wind in its sails. The 45 per cent of Yes voters have rallied behind the party, quadrupling its membership to 100,000.

The likely victims in the general election are Labour in Scotland. The SNP currently sends only six MPs to Westminster, Scottish Labour 41. On present polling, that looks likely to tip to the nationalists, putting them in a strong position to be king -makers in the event of a hung parliament with Labour as the biggest party.

I wonder whether, besides the policy outreach on schools, she’s come on a diplomatic mission to restore good feeling between Edinburgh and London after a scratchy campaign which often cast the English as oppressors. “I don’t come with an olive branch to London because what I’m representing is not hostile to England.” Sturgeon replies. This sounds bracing, rather than ego-massaging for the capital, though she insists she “loves London. But it needs a balance in Scotland”.

She’s been an SNP activist since she was a teenager, growing up in the Ayrshire new town of Irvine. At Glasgow University she studied law and taught herself to debate. Not everyone speaks highly of Sturgeon’s rat-a-tat style of argument but most who know her admire her tenacity.

I suggest one reason why the relationship between the south of England and the Scots has become testy is the view that it get more in public spending than it brings in through revenues (depending on how your account for North Sea oil), but that the response has been a demand for more powers rather than rapprochement after the close-run independence vote. Sturgeon moves into full table-tapping mode. “We pay our way and I passionately refute the notion that we are simply in receipt of subsidy.”

Are southerners unfair to Scotland’s economic reputation? “Hugely unfair,” she says. There is a kind of blazing righteousness to all this, though the omissions are glaring. Not to put too fine a point on it: the SNP has a huge spending programme, on social care, free university places and a health service struggling to meet the needs of an ageing population, combined with a looming demographic fall-off in the workforce, an inflexible approach to public service reform and a falling oil price. But she insists that there is “no over-dependence on oil”. “It’s a myth.” There is a Scotland which sounds awfully like a projection of Sturgeonland — a place where the stuff of running cash-strapped democracies is blurred.

The subject most likely to determine how smoothly or otherwise relationships between England and Scotland develop from now is the balance of Scotland’s desire for more say over its affairs and the English backlash. She infuriated some at Westminster by saying that Scottish MPs should have a say on English laws (such as any changes to NHS funding). But that looks a lot like Scottish MPs requiring a say in any English matter that might be seen to affect their constituents — while Scotland gains added devolutionary powers.

What else might she consider Scottish MPs should vote on? “Tuition fees in England,” she says. “Or anything that reduces spending in Scotland or where there are budgetary implications.”

The line between purely English laws and the rest is, she thinks “hard to draw”. It sounds frankly like a nightmare for the next government at Westminster, with a promise to enhance Scottish devolution on the one hand and the SNP on mission creep.

Having ruled out any dealing with the Tories, she says it is “unlikely we would find ourselves in a formal coalition with Labour”, but would prefer an arrangement in which the ruling party had to “win arguments to secure the SNP’s vote”. Why on earth would Labour accept such instability? She turns the question around neatly. “Ed Miliband would have to explain why he turned his back on the agreement and why he would not pursue a progressive political alliance; why he would prefer to let the Tories govern,” she replies.

But there are thoroughly progressive tensions. Sturgeon is an avowed nuclear disarmer who cannot imagine “any unstable, dangerous or tense situation that would be made less so by the presence of nuclear weapons”. Putin’s incursion into Ukraine does not change her view. “It would not have been better had Ukraine had nuclear weapons,” she says. This might not cut much ice in Kiev, whose leaders are wondering about the wisdom of having forfeited warheads as Russian-backed separatists colonise swathes of the country. Trident renewal would pass muster in Westminster — but not with her votes.

I ask how her relations with the party leaders in London are faring. David Cameron? Lips are pursed. “Cordial and constrictive,” she replies. Blimey, that bad? Ed Miliband? “There are plenty of people who think the party should move a bit further to the Left.”

Mr Miliband’s main electoral challenge in May is seldom seen as being insufficiently red. Yet Labour, she says, should be “truer to its founding values”. Does she stop to ponder why the independence vote was lost? She says the “scare tactics” worked in the end. The more abrasive side of the campaign left an awkward residue in the Anglo-Scottish relationship, I suggest. “Abrasive? Scots?” she says, with a rare droll glint. “The country’s a lot better off for the referendum.”

It sounds like she wants to go through it all again. She thinks independence will come “in five or 10 years, though there are factors, like an ‘out’ vote on EU membership that could hasten it”. As for the aftermath of that Indyref, “the legacy of it will be felt”, she says.

It does sound a little bit like threat, wrapped up in enthusiasm.