After the televised leaders’ debates before the 2015 general election, one of the most Googled queries was: “Can I vote for the SNP?” And although that might have sounded like a straightforward enough question, most of those asking it were in England.

At the time, the Scottish first minister and SNP leader Nicola Sturgeon was asked if she might take advantage of that interest and field candidates south of the border and sensibly she dismissed it. But now – in the course of a rather fawning interview by the actor Alan Cumming – it seems she’s having second thoughts.

And it’s not as wild a scenario as it might appear. In the general election of 1885 a journalist called TP O’Connor was returned for both Galway and the “Scotland division” of Liverpool. An Irish Home Ruler, he opted to sit for Liverpool, which had a large Irish population and, remarkably, he continued to represent the city as an Irish nationalist until 1929, seven years after most of Ireland had seceded from the United Kingdom.

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That, however, was clearly down to constituency demographics and the candidate’s charisma. Sure, English cities such as London and Liverpool are full of Scots, but they aren’t concentrated (or indeed nationalist) enough to give the SNP any realistic chance of electoral success. Then there’s the old steel town of Corby, known for its large Scottish population, but in an informal referendum in July 2014 “Little Scotland” decisively rejected independence.

Sturgeon’s rationale in her Big Issue interview, meanwhile, was unintentionally revealing. She said a lot of English voters who contacted her felt “completely disenfranchised” because there was “nobody speaking up for them”. Now presumably the first minister didn’t mean Tories, Corbynistas or Brexiteers, and arguably Tim Farron’s Liberal Democrats are already “speaking up” for remainers.

So that leaves moderate Labourites without a political voice. I say “revealing” because this is the very constituency the SNP leader and many of her supporters have devoted considerable energy to denigrating over the past few years. Even before Iraq provided a (justified) basis for cynicism, Scottish nationalists denounced the former Labour leader as a pale imitation of Margaret Thatcher. To this day, the terms “Blairite” or “Red Tory” are used pejoratively by supporters of independence or the SNP.

Which is ironic, for the party that the contemporary SNP most closely resembles is New Labour, displaying the same professionalism, constant campaigning, ideological flexibility and elevation of newspaper headlines over substantive policy that gave Tony Blair three successive election victories. Of course that’s not how it appears to many of those who view the first minister as some sort of political saviour; from a distance all they hear is rhetoric about social justice and opposing “austerity”.

Drill a little deeper, however, and they might be disappointed. Next year the SNP will have been running Scotland’s devolved government for a decade without any transformational change to its credit, certainly nothing that could be described as redistribution of wealth. By contrast, after 10 years in power the much-derided Blair administrations had introduced tax credits, a minimum wage and reduced child and pensioner poverty.

The SNP’s standard defence is that it lacks all the “levers” necessary to affect substantive change, yet the more power is devolved to Holyrood, the more conservative the Scottish government seems to become. It recently delayed assuming responsibility for more welfare responsibilities, while prior to last May’s Scottish parliament elections Sturgeon adopted George Osborne-like arguments against restoring the 50p rate of income tax. There is a sizeable gulf, in other words, between rhetoric and reality.

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For deep down, the SNP is about as leftwing as Harold Wilson or Blair, ie not very. Fundamentally, it isn’t driven by ideology but by the pursuit of independence, and over the decades it has adopted whatever philosophical guise is necessary to achieve that goal. In the 1940s and 50s, for example, nationalists were suspicious of the NHS and welfare state; today they pose as its defenders. And the party’s fiscal thinking – such as it is – amounts to little more than trumped-up trickle-down economics.

The first minister should also be careful about reading too much into her email inbox. Two recent accounts of the European referendum, by Sir Craig Oliver and Tim Shipman, both allude to nervousness in the remain camp about how Sturgeon was likely to come across to English viewers in one televised debate. Although popular across the UK at the previous year’s general election, by the spring of 2016 the SNP leader had taken on a more Marmite quality, not least because many voters south of the border found her defence of one union (the EU) but rejection of another (the UK) understandably confusing.

So even if it was tongue in cheek, the idea of the SNP trying to emulate TP O’Connor’s nationalist success in England smacks of hubris, symptomatic of a party convinced of its own moral and political superiority. And hubris, of course, can mean pride before a fall.