This is the Indian summer of Vince Cable. He had long nurtured ambitions to lead his party, but finally gave up on them when he was one of the casualties of the 2015 election massacre of the Liberal Democrats. He took his ejection from parliament to be the death of his political career.

“If you’d asked me six months ago, I assumed my exile was permanent,” he smiles. So he threw himself into a post-political life. He tried his hand at writing a thriller. He traded on his training as an economist and experience as business secretary in the coalition years. “I was going around universities being a wise man.” Though he had made a promise to his local party that he would stand again for the Lib Dems in Twickenham if there were an early election, he assumed it wasn’t a pledge that would have to be redeemed. “I was also doing ballroom dance competitions in Blackpool. I’d established quite a good new lifestyle.”

Then came the snap election, the departure of Tim Farron as Lib Dem leader after the party’s disappointing performance and the resurrection of Cable as an MP. A decade after he had ruled himself out of running for the job on the grounds of his age, he became party leader at 74.

Looking at the beaten-up state of the Lib Dems, some might wonder whether it was worth sacrificing that “good new lifestyle” he enjoyed out of parliament to take charge of a party that has only 12 MPs and is flatlining beneath 10 points in the opinion polls. “There is this old expression, ‘there’s nothing as ex as an ex-MP’. You are aware of it. I realised when it came to the crunch, I did miss being part of the action.”

Much is written about the hunger of young ambition. Cable is an example of how old ambition can be even hungrier. After such a long wait for his chance to lead, and knowing as he must that he doesn’t have all the time in the world, here is a man in a hurry. He looks energised, rather than daunted, by the challenge of dealing with what some of his colleagues call an “existential crisis” for the Lib Dems. “It’s pretty dawn to dusk stuff,” he says cheerfully of his life as leader. “I go to bed late. I go to bed very late.” One Lib Dem peer recently complained that Cable was still firing off emails about this or that long after midnight. So he stopped sending the emails – and started sending post-midnight texts instead.

He is the oldest person to lead a British political party since Winston Churchill. “In the first two days after I became leader, the questions I had from journalists were all about age. Hardly anybody has said a word about it since.”

‘In the first two days after I became leader, the questions were all about age. Hardly anybody has said a word about it since.’ Photograph: David Levene/The Guardian

After a period when party leaders got more and more youthful, the trend has suddenly reversed. Theresa May is older than David Cameron. Jeremy Corbyn has decades on Ed Miliband. “I think it’s largely a coincidence, but to some extent events have removed the taboo on age. When things have been screwed up and we’re in a mess, people who have shown a certain amount of endurance and resilience, those are the kind of qualities that people value a bit more maybe.”

When he became leader, there was a notion around that Cable would be a caretaker for two years or so and then hand over to a younger torch-bearer, who most presume would be the party’s deputy leader, Jo Swinson. “No, that wasn’t the case,” he says, bluntly rubbishing the idea that there was a succession deal between them when she decided not to run for the top job. “I’m not putting up a limit. I do it for as long as I need to do it.”

One of his tasks at the party conference in Bournemouth is simply to lift morale. Though the Lib Dems received a surge of new members following the Brexit referendum, this did not translate into a boost at the June election. Their vote was down even on the slaughter they suffered in 2015. His priority is “getting up the vote share” from its current miserable level. “When we’re in single figures, there is an issue about how credible we are. I’m trying to get more and more exposure and trying to get more definition. Get some clear messages across. The key thing is to get our own troops and the public perception back to the idea that we can win.”

He identifies “two strands” to his attempt to revive the party. “One of them is issue based.” The Lib Dems will have clear things to say about addressing inequality and inter-generational unfairness. “The other is projecting the idea that I’m an alternative prime minister.”

We clearly look incredulous, because he then insists: “You may blink, but that’s the message I need to get across and want to get across.”

It is true that we live in an era of extreme volatility where yesterday’s unthinkable can become today’s reality, but all the same. To go from a dozen MPs to No 10 sounds, ahem, on the ambitious side. Him as prime minister? Really? “Given the alternatives, I think that’s plausible,” he contends.

He cites Emmanuel Macron’s victory in France and Justin Trudeau’s rise to the premiership of Canada as evidence that “in these times of political upheaval all kinds of strange things can happen”.

While even the most optimistic Lib Dem may struggle to share his belief that he could become prime minister, this assertion does illuminate how he wants to lead the party. Under Farron, the Lib Dems fell back on their old tradition of being essentially a party of protest. Cable has no time for that, seeking to pitch them as a potential party of government.

“We haven’t been seen as even bidding for that ground,” he says. “Being a plucky third party is not my view. It’s got to be that we are a serious party with a serious leader who can run the country.”

The more realistic prospect is that they might at some point in the future find themselves again in coalition. “I can’t see it at the moment,” he says, “but you can’t indefinitely rule it out. Not under the present leadership [of the Tories or Labour] and not under the present circumstances, but in the longer term – who knows?”

Cable has already started setting out a policy stall that concentrates on fairness and opportunity. He puts emphasis on doing more for the less affluent by taxing wealth, a strand of Liberal thinking since John Stuart Mill.

“We have to be in favour of the taxation of wealth. Otherwise, fighting inequality doesn’t mean a great deal,” he declares.

Cable started his political career as a Labour councillor in Glasgow in the 1970s and then joined the moderate breakaway to the SDP in the 1980s. He has always been on the social democratic wing of his party. During the coalition years he was the Lib Dem member of the cabinet who found it most conspicuously uncomfortable being in government with the Tories. His emphasis on inequality is consistent with his career. But we suggest that there is a big problem here. Why would voters who want less inequality and an end to austerity choose the Lib Dems when they can go the full Jeremy Corbyn?

“You’ve got to have hope and you’ve got to have realism at the same time,” he responds. “You’ve got to have economic literacy as well as progressive instincts. We can do both.”

Corbyn, he argues, can’t offer that combination because “a lot of the talk is still very much 1970s kind of soft Trot, as we used to call it in the battles in the Labour party. ‘We support strikes to break the pay cap.’ That’s old, hardline Bennite stuff. But I know there are a lot of good people in the Labour party who are trying to recapture some of what you and I would call social democracy. Those latent fundamental divisions between revolutionary socialism and social democracy are going to play out.”

He is “not predicting mass defections” from Labour to the Lib Dems, but “there are a whole lot of issues where the big schisms in the Labour party could well reappear”.

One continuity with his predecessor is to define the Lib Dems as the party of “exit from Brexit”: unequivocally opposed to leaving the EU and pledged to a referendum on whatever deal the government finally negotiates. He will be joining an anti-Brexit march on the Tory party conference, busting the convention that leaders do not mount protests at the conferences of rival parties. “Yes, I’ve become a marcher again. I used to do this in my youth. I’ll be speaking to the march, I’ll be doing my Jeremy Corbyn on a soap box.”

Their anti-Brexit pitch was a disappointing failure for the Lib Dems at the election. Though 48% backed remain in the referendum, the Lib Dems ended up with a vote share of less than 8%. This, he thinks, was because it was “premature”. Back in June, “the minute I hit the doorsteps, I realised it wasn’t quite on target. The remain constituents were saying: ‘We’ve had this referendum. We don’t want another one. Just for the moment. Let’s just get on with it, see what the government can do. And the problem with the phrase ‘second referendum’ was it did look as if you were trying to run it again.”

“We’re now in a very different situation,” he adds, “and I think what we’re saying will resonate.”

He is in regular discussion with Labour MPs about how to coordinate opposition to the government. That includes a recent and lengthy discussion with Keir Starmer, Labour’s principal spokesman on Brexit. On many of the crucial questions facing parliament, the key to the outcome will be whether there are enough Tory MPs prepared to join hands with the opposition parties to amend the Brexit legislation in defiance of their own government. “That’s the big uncertainty over the next six months. Whether there will be a critical mass of them. It will take quite a lot to get those people to rebel.”

Talking to Cable, you get the strong impression that he thinks the parliamentary struggles cannot deliver a softer Brexit because it is not really available as an option. It is “wildly implausible” that “the Europeans will keel over and give us a pretty good deal”. It is “much more likely that the soft Brexit option, the smooth transition, will just never happen. There’s too much division in the Tory party over it.” He points to the latest intervention by Boris Johnson – “the Poundland Donald Trump” – as an example of the forces in the Conservative party pushing for an “extreme Brexit”. Even if May now wants a softer Brexit, “her position is very weak within her own party, not just in terms of numbers in parliament. I can’t see that happening.”

“So we are faced, whenever the crisis point comes, with extreme Brexit. We crash out. Or you have exit from Brexit. And then, who were the people who said this is going to happen? And who are the people who’ve got an answer to it or at least a way forward?”

At that point, or so he hopes, his party will receive its reward in public esteem for being the people who have always warned that Brexit was a disastrous idea. It may be a while before that happens, but then one thing this Lib Dem leader knows about is waiting for his chance.