A thick, green arch of privet, honeysuckle and ivy obscures the entrance to Vince Cable’s home. The veteran Liberal Democrat and former cabinet minister has lived in this London town house since he moved to the capital from Glasgow University in 1974. It’s in the heart of Twickenham, the affluent west London constituency he represented for 18 years before the Conservatives defeated him in 2015.

Twickenham Stadium’s steel criss-cross roof looms above us. “I grew up watching rugby league so it’s not in my bloodstream,” he says, smiling, as he hovers in the hallway.

Cable was raised in York by working-class parents who had jobs in chocolate factories. You can still hear the occasional Yorkshire vowel in his southern accent.

As he potters around his house in a crisp, white shirt and navy suit trousers, his slippers are the only hint of a quiet afternoon. But he won’t be relaxing for long. Not only was he re-elected to parliament last month; he is also expected to become the new leader of his party. He will likely be unopposed, after a disappointing election for the Lib Dems and the resignation of Tim Farron. Trying and failing to appeal to Remain voters, the Lib Dems won only 12 seats.

The manifesto called for a second referendum on the Brexit deal. “It didn’t really work,” Cable says. “People thought we were trying to rerun the last referendum and wouldn’t accept the result, whereas actually we’re saying . . . if we’re faced with a bad outcome, or no outcome, then the public should have an opportunity to move back into the European Union.”

As leader, Cable will continue pushing for this. “It was a very good message for 2020 but not for 2017,” he says. He views anti-Brexit sentiment as a waiting game; if the economy suffers, people will see the Lib Dems as the only true pro-European party.

Having served as business secretary in the coalition and made prescient remarks in the Commons ahead of the financial crisis, Cable is relying on his economic credentials. “Over the next couple of years or so, I think we’ll begin to see real damage being done,” he predicts. “I will just relentlessly hammer home that point.”

We settle in his front room, which is festooned with decorative rugs, wooden statues of Hindu gods and intricately embroidered throws and pouffes. The vibrant decor is a legacy of his late wife, Olympia, who was Indian. Two wedding bands glint on his ring finger – he remarried in 2004 – as he fiddles with his glasses while we talk.

In the late 1960s, Cable returned to Britain with Olympia from Kenya, where he had worked in government for two years. “[We] immediately walked into the ‘rivers of blood’ speech and all the hatred around that, and it was absolutely dreadful,” he recalls, shifting on his leather sofa. “You felt it. It was really nasty.”

Cable believes the EU referendum campaign showed that it is “not difficult to stir up these feelings all over again”. Because of his first wife, he has “always been conscious that that’s lurking in the background”.

So how did he react to his former cabinet colleague Theresa May condemning “citizens of nowhere” in her Conservative conference speech last year?

“I thought that particular phrase was quite evil. It could’ve been taken out of Mein Kampf,” he replies. “I think that’s where it came from, wasn’t it? ‘Rootless cosmopolitans’? It was out of character for her.”

But Cable wishes to move his party beyond Brexit. In particular, he feels that the Liberal Democrats have failed to mobilise young people. “We have to address – and the Labour Party has so far addressed it much more effectively than we have – some fundamental injustice between the generations . . . and to have an offer, to have an approach, which is attractive again to young people.”

But Cable is 74 years old. Is he the right leader to attract youth support? “There was a phase – was it 20, 30 years ago? – when there was a faith in youth,” he says. “You know, Tony Blair, Nick [Clegg] and others. And the mood has changed. It’s more sober. People are puzzled and angry . . . and I think they’re willing to listen to people who’ve got some experience, some historical memory, of the way things are.”

He cites Jeremy Corbyn, Bernie Sanders and even Donald Trump (“I hate to use Trump as an example, but he’s touching 70”; Trump is 71), as well as Britain’s first Liberal prime minister: “The great William Ewart Gladstone was 82, I think, when he won his last election.”

Yet many Lib Dems say that it’s time for a younger, fresher face. There was widespread disappointment that Jo Swinson, who could have been their first female leader, didn’t stand. Cable praises Swinson, who will be his deputy, but he insists that he is “not standing as a caretaker”.

“Gender isn’t an issue any more, rightly so,” he adds. “Thanks to Obama, race isn’t really an issue any more – at least, we hope not. And age shouldn’t be, either. It should be who you are and what you have to say.”

A big test for Vince Cable’s leadership will be whether he is still associated with the 2010-15 Tory-led government and the tuition fees betrayal. “Coalition nostalgia is creeping in,” he claims, but he still warns against a coalition with the Tories or Labour. “I have the metaphor of mating with a praying mantis,” he says, as his pale blue eyes twinkle with amusement. “You get eaten at the end of it. We don’t want to go down that road again.”