When Jo Swinson announced in June that she would run for deputy leader of the Liberal Democrats, rather than leader, she used a vivid analogy: “Creating lasting political change is a marathon, not a sprint.” (She also noted: “Most blokes in my shoes would run for leader like a shot.” Sir Vince Cable, 74, duly did so.)

At 37, Swinson is a veteran of several marathons, starting with one around Loch Ness in October 2007, when she spent the journey to the course preparing posters for the “election that wasn’t”. It began a tradition of her running being interrupted by political life.

This year, at least, she felt she had plenty of time to prepare for the Stirling marathon on 21 May. After losing her East Dunbartonshire seat to the SNP in 2015, she had spent time thinking about her life, helped by Herminia Ibarra’s 2003 book Working Identity, which describes unusual career changes, such as a psychiatrist who became a Buddhist monk. Swinson’s own transformation was less eyebrow-raising: she began writing a book on gender inequality, to be released next year, which draws on her time as minister for women and equalities in the coalition government.

Then Theresa May called a snap election on 18 April. “I knew in a heartbeat what I wanted to do,” she tells me in her office in Portcullis House, looking out on to Big Ben. “And I knew I could do it.” (On 8 June, she reclaimed her seat from the SNP with a 5,339 majority.)

The election was less brutal than she expected – “or maybe I’ve just got a thicker skin” – with no repeat of 2015, when her mum's car was vandalised in the run-up to polling day. “Was that because of the election, because she had a Swinson poster in the window?” she asks now. “Was it coincidence? It’s never been vandalised in the three decades before.” She adds: “There’s a level of vitriol in Scottish politics where I hope we can put the genie back into the bottle, but it’s hard. It’s unhealthy for democracy.”

Now, as deputy leader, Swinson will need all of her stamina as she tackles two connected issues: first, the slow, grinding process of scrutinising Brexit in the Commons, and second, getting a hearing for the Liberal Democrats, given the party has just 12 MPs. It is one of the strange quirks of the election that many anti-Brexit voters went to Labour, despite Jeremy Corbyn’s own Eurosceptic inclinations.

Swinson believes the Remain campaign failed because of its lack of emotional resonance; the only time she felt moved, she said, was in the last days of the campaign when the actor Sheila Hancock “talked about the experience of living through the Second World War, and what that meant, and what Europe meant”.

She says the Lib Dems need to find that register again to convince people that we need a second vote on the terms of the deal – in the country, not just in parliament; and on continued EU membership v the proposed deal, rather than comparing it with no deal at all. “The only way to secure our place in the EU,” she notes, “is a change in public opinion.”

Over the summer, she talked to an academic from Birkbeck University who told her that one question predicted a voter’s attitude to the EU better than any other metric, even income. It is this: “Do you think it’s more important that children should be well-behaved, or considerate?”

The question has been around since 1992, and it measures an axis not picked up by conventional ideas of left and right. Rather than economic and social issues, it suggests the big split in modern politics is between authoritarians and liberals. However, she adds: “I’m the mother of a toddler; frankly, either would do.”

One problem with this axis – which is also described as “open v closed” – is that “it’s not like there’s one economic or social policy that’s going to sort it out”. Another might be, on the evidence of the Lib Dems’ dire poll ratings, that there are far fewer liberals about than we assumed.

Swinson’s party is also hamstrung by its time in coalition with the Tories. Echoing Nick Clegg, who has called the vote to raise tuition fees a “mistake”, she says that it was inexperience that led her party to agree to the measure. “The mistake was before we got to the vote,” she says. “We should have reopened the comprehensive spending review.” (There’s a parallel here with Harriet Harman’s exit from the first Blair cabinet for pushing through welfare cuts; she wishes, she says in her autobiography, that she’d had the courage to tell Gordon Brown to find the savings elsewhere.)

The Lib Dems also suffered during the election campaign because of the relentless focus on Tim Farron’s Christianity – specifically, whether he thought gay sex was sinful. Given that Jacob Rees-Mogg has just had the same pushback for saying that abortion is always wrong, isn’t there a case for saying that it is impossible to be a high-profile politician if you have strong Christian views?

“There is a big difference between Tim Farron and Jacob Rees-Mogg in that regard,” she says. “Tim Farron voted for gay rights and Jacob Rees-Mogg has voted to restrict abortion.” Swinson, a humanist, says that having experienced pregnancy herself, she finds it hard to understand how “to force someone to go through all that… not to see how that isn’t itself a massive ethical quandary.”

Swinson has just finished Naomi Klein’s polemic No Is Not Enough. However, she is resolute in her belief that we are currently too tribal – and too cynical. Trying to overturn the current anti-politics mood, however, will definitely be a marathon, not a sprint.