At a circular table in a glass-walled kitchenette inside the Scottish National Party’s Edinburgh headquarters, First Minister Alex Salmond is bullish about his party’s prospects at the impending general election. We find the formidable party leader on a busy afternoon: the Scottish Parliament dissolved the previous day, and Tory chancellor George Osborne announced his new budget only a few hours before our meeting, Salmond is taking to the campaign trail with characteristic fury: polls show Scottish Labour putting up a staunch electoral fight, and the SNP are in the midst of a relentless media blitz by way of a counter-offensive.

They’re in a prime location from which to do so: the SNP’s open-plan command centre is tucked away on an unassuming Holyrood wynd, but it’s wired straight into the Edinburgh media complex. Rupert Murdoch’s News International have their offices upstairs, and from the front door you can just make out the Scotsman building. The BBC’s capital outpost, meanwhile is just across the close — and it is from here that Salmond has just come as he strides in to greet us with a firm, double-fisted handshake. Flanked by a party aide who remains at his side throughout our time together, the First Minister sets on the table in front of him an old and very well-thumbed BlackBerry and a list of talking points headed ‘SNP achievements on education’. The young staffer next to him has a stack of similar policy crib-sheets, presumably left over from the day's previous appearances.

It is a blunt reminder of Salmond's innate sense for his audience: he has a knack for making the issue at hand seem like his foremost priority. Among students, for example, he lambasts the Westminster government for rolling back state involvement in higher education ­— an idea he laments as “another ridiculous, absurd mistake, and deeply damaging to long-term prosperity”. Salmond is forceful with his belief in activist government: “I don’t believe you can finance higher education by either private donation or private wealth,” he remarks, with a wry jab at the largely privately-educated coalition Cabinet, Salmond does not deny that non-Scottish students are likely to be worse off if he is re-elected. “We removed [fees] in Scotland, and we’re not going to reintroduce them. As I famously said: the rocks will melt in the sun before I have Scottish students paying tuition fees. But I can’t finance English students in Scotland,” he says — with regret that seems genuine. “I can’t do that. I wish I could, but I can’t, and I can’t finance European students to the same extent that they've been financed."

Nor does Salmond deny that on specific questions of higher education policy, he has few definitive answers yet: he cannot put a precise figure on Scottish tuition fees, saying only that “we’ll try and set a figure where nobody will pay more coming for a four-year degree in Scotland than they will for a three-year degree in England.” He hints at a funding model inspired by that of Ireland, where a fixed levy on non-Irish students was deemed compliant with EU regulations. The SNP’s aim, he tells us, is to make Scotland academically competitive — and to avoid a potential influx of ‘fee refugees’. “We’re not going to price Scotland out of the market, as it were, but equally, we want people to come to Scotland because it’s the best education, not because it’s the cheap option.”

But he is quick to dismiss reports of a £200 million funding gap for Scottish universities, and to condemn those who perpetuate that figure. The worst culprit, we’re told, is University of Glasgow principal Anton Muscatelli, “the Labour Party’s favourite economist.”

Discussing the budget, Salmond becomes unusually ruminant, a professorial air the legacy of his first career as an economist. “We need a different approach,” he says, advocating “a big increase in capital spending... The defence of the government is that they’ve just adopted the same capital plans as the Labour Party did, but the Labour Party were wrong.” Salmond doesn’t give ground easily, and even on those budget measures he agrees with, he damns with faint praise.

Moreover, he revels in his new-found freedom from the strained politeness of Parliament, and the campaign affords his notoriously sharp tongue plenty of targets. The Liberal Democrats at Westminster were “hoodwinked” by their Tory coalition partners, he says, disdainfully, and their leader Nick Clegg “suddenly became the greatest enthusiast in the world for fiscal orthodoxy.”

The hapless deputy prime minister seems to particularly frustrate Salmond. “I had to sit and listen to him in the meeting where he was telling us all how the wool had been pulled from his eyes and he’d suddenly realised the extent of the criticality of the UK’s finances, and how he was frightened of a Greek situation developing,” he recounts with an exasperated sigh. “Actually, the wool was pulled over his eyes. There was never a substantial danger of that occurring, and the degree of fiscal retrenchment that he was prepared to swallow was not necessary.”

But what about his rivals at home? Despite polls forecasting a bitter fight on 5 May, Salmond seems unfazed: Labour in Scotland, he opines, are past their prime. Reeling off a list of larger-than-life Labour figures, he interrupts himself with character reviews: Donald Dewar (“a difficult person to like... but hugely talented”); George Robertson (“never really got on with him - Lord NATO, as I used to call him... but a talented guy”). He continues — John Reid (“a bruiser, but a talented politician”); Gordon Brown (“a substantial politician... [but] he wasn’t the right person to be prime minister”) — and, with no small satisfaction, concludes that “the problem for the Labour Party is that they’ve had a generation of believing in nothing.”

Conversation with Alex Salmond is a curious experience. Current psephology paints him as a divisive politician facing a potentially bruising election in a matter of weeks, but the man opposite us is calm: he looks tired, but with a cheeriness that seems to suggest he knows something the pollsters don’t. “Four years ago, to be absolutely ruthless about this,” says the veteran political brawler, “the only person most people knew in the SNP was me. That’s no longer true: people know who Nicola Sturgeon is, they know who John Swinney is. These are substantial people, and regarded as such.”

Government has been hard: the independence agenda has stalled, and the SNP have suffered harsh defeats on alcohol pricing and the Edinburgh trams. But there is no hesitation when he is asked about his time in office. “I love it - I’m applying for the job again. I’m Alex Salmond, and I want to be First Minister again.”