OBVIOUSLY, I need to ask Jo Swinson about her controversial policy of revoking Article 50, but there are other interesting things to talk about first. Such as who she’d rather have a cup of tea with – Nicola Sturgeon or Nigel Farage. And whether she thinks the Lib Dems really can end the SNP’s domination of Scottish politics. And what she learned from the man she met on the train last night.

The train was the sleeper from London to Glasgow – Swinson was catching it after a busy week in which she delivered her first speech to the Lib Dem conference as leader. A woman on the platform told her she used to be Tory but was now Lib Dem. Another man said “great speech”. And in the dining car, a Scottish man told Swinson he used to be a different shade of yellow. “He had obviously moved from the SNP,” she says. “And that wasn’t happening to me in the past.”

Of course, Swinson recognises that a man on a train does not equal a scientific trend, but she does think something interesting is going on. The 39-year-old leader of the Lib Dems grew up in Glasgow in the 80s and 90s when Scotland was dominated by Labour, but the domination, she says, turned out to be much less strongly rooted than people assumed. “I suspect the same is true of the SNP,” she says. “The situation is not ‘my parents did this and I’m for this party through and through’. People have changed and once people have changed once in a vote, it’s easier for them to do that again.”

But we need to talk about the practicalities of that idea. I’m meeting the Lib Dem leader and MP for East Dunbartonshire in the centre of Glasgow on the day of the climate protests in George Square. Swinson was at the event and is still holding her placard, which she made herself from cardboard and tinfoil. “Love Earth” it says. Nice slogan. But isn’t “Vote Lib Dem” a much trickier slogan, especially in a first-past-the-post system? What, for example, does a Remainer and Unionist do in a seat that’s split between the Tories and the SNP?

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Swinson insists the Lib Dems can win those kind of seats. “The SNP went from 6 seats to 56 seats and that was something people would’ve previously said couldn’t happen. There’s an ability to win a seat from third place. Some of the recent polling has shown that, in say Ross, Skye and Lochaber, we’re the ones challenging the SNP.”

Swinson also thinks part of the appeal of the Lib Dems at the next election will be their unequivocal support for the Union. “I look around,” she says, “and see Labour trying to do a deal with the SNP for indyref2 and I see the Conservatives doing what they’re doing and we’re the ones standing up and saying our United Kingdom is really important. The 300 years of shared history, the prosperity and the culture and the ties we have across borders. Those are really valuable. A few years ago, lots of parties were making that case; now it feels very much that it’s fallen to the Liberal Democrats to make.”

I ask her if she’s ever had any doubts about that position, but she says the opposite: she’s more determined than ever in her support for the UK. “I’m more determined because, when you saw that Brexit vote happen and now we see what it’s led to, it’s been a textbook demonstration of why breaking up is hard to do and the type of chaos we’d be mired in if we were suddenly in independence negotiations. The interlinking of the 300 years of union has been much, much deeper than the 40 years of European union.”

But what about the argument I hear from SNP supporters that independence is simply a case of self-determination? Swinson’s response is that it’s better to work together on shared solutions, and she takes a similar view on the argument that Scottish nationalism is more civic and benign than other forms. Both Scottish nationalism and English nationalism, she says, try to make people choose between the identities of Scottish, British and European.

Does that mean she thinks Scottish nationalism is the same as English nationalism? “Would I rather have a cup of tea with Nicola Sturgeon than Nigel Farage, yes,” she says. “But ultimately, it’s about exceptionalism for one nation and trying to define around that nationhood rather than being more open to those people that are our closest neighbours. Ultimately, Scottish nationalism still wants to break up the United Kingdom and, even when it says ‘Scottish nationalism is different’, there’s an exceptionalism which sort of says ‘we’re better than the others’ which, as a humanist, I don’t believe that. I love Scotland. I love Britain. I don’t think that makes us better than other people elsewhere and we should be working with them and we can achieve more together. So it’s that openness that’s important.”

This position means Swinson thinks a second independence referendum is a bad idea, but it’s here that we get into more complicated territory. The Lib Dem leader has effectively committed her party to ignoring the result of the 2016 EU referendum after winning an election, so doesn’t that make it harder for her leader in Scotland, Willie Rennie, to demand that the SNP respect the result of the 2014 Scottish one?

“I don’t think it does,” says Swinson. “We have a very consistent position – we’re saying we believe the best future is for Scotland to be in the UK and the UK to be in the EU. That is an entirely consistent position. It’s what we believe to be the case and we’re acting in a way that we think is to protect Scotland’s best future.”

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However, there are other apparent complications with Swinson’s position on the EU referendum. For a start, isn’t she effectively cancelling the votes of the millions who voted for Leave? No, she says, she is still in favour of a people’s vote but, if there’s an election, voters deserve the chance to choose an alternative to a no-deal Brexit.

“We would go into an election,” she says, “and say to voters if you elect a majority Lib Dem government, we will revoke Article 50, and it’s only if people vote for that, in such numbers that we elect a majority government, that is what we’d do.” So, she would impose a policy based on a win under first-past-the-post, a system the Lib Dems despise? “You’re not going to find anyone that’s more in favour of changing the voting system than me,” she says. “I would just say that the people who are arguing about this now have not exactly joined our chorus of campaigning for electoral reform.”

In the end, says Swinson, her policy is about taking what might be the last opportunity to fix the fall-out from a referendum she says was called by David Cameron for party political motives. But I ask her whether the causes of the current mess don’t run deeper than that. Part of the reason so many people voted Leave is they were hoping for something better than the austerity imposed by the Lib-Dem/Tory government of which Swinson was a part. Doesn’t that mean that, in supporting austerity, she was partly responsible for the referendum in the first place?

“The problems in our society date long before that,” she says. “There are two main drivers for the Leave vote – one was the economy not working well enough for people and the other is cultural factors, including nationalism and feeling uncomfortable about change. Life was really hard for people but Brexit isn’t the answer.”

It’s obvious, though, that the subject of austerity is not easy territory for Swinson – in fact, it’s when she talks about the coalition that she most clearly shows signs of discomfort. Swinson was a minister in the government and voted for policies such as the bedroom tax and I ask her if, a few years on, this is a difficult memory for her and whether the cuts went too far.

“I recognise that we didn’t get everything right,” she says. “We should have been ramping up the investment at a much earlier stage in the coalition but we got there. What we delivered was Labour’s spending plans so for all we get attacked by Labour on this, if you look at what happened, it’s basically what Alistair Darling had set out. And I don’t think it’s credible to say there shouldn’t have been any reduction at all when we did have a deficit that was 12 per cent.”

And Swinson still thinks that, in principle, working together across parties is a good idea even though she’s ruled out a coalition with Boris Johnson or Jeremy Corbyn. She would, however, be up for an alliance with the Scottish nationalists to maximise a Remain vote in any general election, although she says the SNP have already said no.

“I suppose,” she says, “the idea that you work with people in other parties to try to achieve things I think is a good principle in politics. There are some who suggest that some people are inherently evil because they have a different political philosophy.” But she doesn’t think that? “No. Sorry if that’s a controversial thing to say, but I think we disagree and I don’t think it really helps to position people in that way.” Tories are not evil. An interesting idea. But could it ever catch on as a slogan?