It's probably no coincidence that the MP the nation fell in love with not so long ago is less like a politician than any I have ever met. For a start, Vince Cable is the first secretary of state I've known to travel in standard class on ministerial business. I find him in wedged into a crowded carriage at King's Cross, looking rather like a university vice-chancellor – cerebral and unworldly, in a slightly crumpled suit, unrecognised and entirely at home in his anonymity. By a happy coincidence, the age of austerity appears to suit the new business secretary's temperament rather well.

"Yes," he agrees almost bashfully. "I don't feel comfortable with luxury, and I try to stay fairly normal. I mean, the first week I became a minister I discovered that there were ministerial cars and Jaguars and all this kind of thing, but I very quickly discovered that a) it's very claustrophobic and you don't get any exercise, and b) I could see it's a rather quick way of getting out of touch. So I reverted to my normal ways of transport."

There has been much speculation that frugality is the only feature of this government Cable will find to his taste. Perceived as the Lib Dem furthest to the left – a former Labour party councillor and parliamentary candidate, the man Gordon Brown phoned in the frantic post-election days – Cable is widely tipped as the minister most likely to resign from the coalition. He made no secret of his preference for forming a government with Labour – but was forced by the arithmetic of the election result to abandon that dream, "and follow my head, not my heart". Anyone who watched Nick Robinson's recent documentary about the five days following the election could not have failed to notice the acute unease in Cable's body language, as he recalled the negotiations that led his party into bed with the Tories.

We're so accustomed to political spin that Cable's unwillingness to conceal his misgivings has been interpreted not as honest ambivalence, but more like tantamount to mutiny. "According to the papers," as he says himself, "I'm miserable, alienated, and on the brink of resignation." For many Labour voters – and a lot of disillusioned Lib Dems too – Cable's resignation would represent some sort of moral triumph, or at the very least, a return to politics as normal. "But that's simply not where I am," he says.

He doesn't strike me as miserable, but there is something touchingly gentle, almost vulnerable, in his bearing – particularly when he produces a sheet of A4 on which he's listed all the things he feels his department has achieved to date, handing it over like a schoolboy submitting his homework. "High-level trade mission to India, with several major outcomes for business, education and science," he has written. "£50m capital fund launched for FE buildings," and so on. If misery and alienation is not "where I am", the challenge is to work out where exactly Cable is.

Cable was elected to parliament in 1997, but as a Lib Dem he never seriously expected to ever find himself in government – least of all with the Tories. When it suddenly happened, he says quite candidly that he didn't think it stood much of a chance. "But the big surprise, which in some ways is a pleasant surprise, is that the coalition does actually work. Personal relationships are very good, very businesslike. Having worked with [the Tories] at close quarters, I've been pleasantly surprised that they're not as I'd envisaged them."

I remind him that he once described chancellor George Osborne as "out of his depth". "I wouldn't say that now," he answers evenly. "Having dealt with him quite closely on the big issues, you know, the budget and so on – no, I've developed, you know, substantial respect." What does he now see in Osborne that he'd previously overlooked? "Well previously we had virtually no relationship at all. You're dealing with people solely in the context of parliamentary banter, you know, not working with people as colleagues, and you discover positive qualities you hadn't seen before." In Osborne's case, what would those be? He pauses for a moment. "Well, I think, you know, very good strategic thinking." Anything else? Cable's voice jumps a few octaves, and becomes oddly detached; not grudging, exactly, but closer to that than effusive.

"Umm, he's clearly able. An able guy. And we work together well." That's not the most ringing endorsement I've ever heard, I laugh. "We've worked together very well," Cable offers. "That seems to me a pretty good endorsement."

The irony is that because Cable's praise is so tepid, observers tend to assume he must be lying. But if he really wanted to mislead, presumably he'd claim they were getting on like a house on fire – so I'm inclined to read his account of coalition relations as more or less accurate. It's noticeable that he refers to his Tory colleagues by their full or last name – it's never just George, or David – but I never suspect him of being less than truthful. He steers a careful course between candour and loyalty – and when this gets tricky, he prefers to become vague.

For example, Cable was opposed to the abolition of the Financial Services Authority – which Osborne has now ordered. When I ask if he's changed his mind, he says, "Erm, I've accepted the arguments. And I think it's a different order of problem to the arguments about bank lending. The bank lending issue is absolutely fundamental to how the economy functions. How you organise the furniture, the quangos and so on, is to my mind a secondary problem." It sounds, I suggest, as if he means he is picking his battles. He laughs. "That's one way of putting it, yes."

He is more forthright in his support for the government's programme of radical cuts. "People forget that a year before the election, I published a pamphlet for Reform which got a flurry of publicity at the time, and was subsequently forgotten, which actually heralded a lot of the things this government has done. So we were aware that there would have to be serious cuts." But during the chancellors' debate in the election campaign didn't he caution against Osborne's plans to start cutting straight away?

"No, I was very careful in what I said. I said we should approach it on the basis of economics and not political dogma, that was the phrase I used. I set out five factors which should determine when you start cutting the deficit, and one of them related to the conditions in the markets. At that time, there was no enormous urgency. But by the time of the election the financial crisis had burst in Europe, and conditions had changed."

Vince Cable arrives at No 10 with Conservative education secretary Michael Gove. Photograph: Peter Macdiarmid/Getty Images

The risk of a double-dip recession remains, he acknowledges, very real – perhaps a little more so in his mind than the Treasury's. "As I recall," he says, "the government's own forecasting risk puts it at something like one in four, one in five." But asked for his own estimate, he says, "Well, you know, certainly well below 50-50," which sounds somewhat higher than one in five.

He says he is optimistic about finding a "progressive" alternative to university tuition fees, and dismisses recent reports of opposition from senior Tories with convincing confidence. Any decisions on tackling bank lending will, he insists, be made jointly by himself and Osborne. But if Cable feels fundamentally comfortable with the coalition's decisions to date, how does he account for the rumours of his unhappiness? "Well, I think there's been a lot of mischief-making in the press," he says wryly – if not quite convincingly. If he wanted to put an end to it, all it would take was a showy display of unmitigated delight. Why not silence the rumours?

"Well," he begins, before pausing to consider his words. "I think the whole situation – well, it's not comfortable. And it would be dishonest to go around like an American politician with a bright grin the whole time, because what we're managing is quite a difficult situation. So I'm just being rather transparent.

"I think what I'm doing is worthwhile, I think I'm making a difference, and so I'm committed to it." He pauses again, and smiles weakly. "But that doesn't mean to say it's, you know, wonderful."

If Cable comes across as an unusual politician on the train, the impression is only enhanced when we arrive at the Corus steel plant in Darlington. Touring a steel beam factory, he readily admits he'd had no idea it manufactured components for some of the world's iconic buildings – the new World Trade Centre in New York, London's Olympic stadium and so on. Later, visiting Teesside University in Middlesbrough, he introduces himself with the self-deprecating admission that, "For someone like me, who went to Cambridge and is surrounded by those kinds of people, we tend to forget what universities like yours are doing." He doesn't pretend to understand every detail of the Corus operation, nor offer flashy rhetoric, or dash about pressing flesh. Spotting a gaggle of local reporters, for a fleeting moment he looks almost daunted

I'd say his occasional self-consciousness stems more from humility than vanity. He has however, occasionally been accused of unduly high self-regard. In Roy Hattersley's words, "Vince thinks a lot of himself." I think I might see what Hattersley meant when I mention Cable's famous joke about Brown morphing from Stalin to Mr Bean, and ask if he knew it would be such a hit.

"No, and in fact I get a bit frustrated, because I'm actually quite good at one-liners, and I've had hundreds of them over the years, and they sink without trace, and I get very frustrated. Every party conference I really work on the speeches, and I always have two or three things I'm quite proud of, and no one ever remembers them. I can't even remember them myself. I think they're brilliant," he chuckles, "and no one else notices. So every week at PMQs I had a very good line, I thought. And yet that's the only one that anyone remembers."

But by political standards, the absence of starry self-promotion is quite striking, and his modest manner goes down well with most of the people we meet. But when Cable emerges from a meeting with union leaders at Corus, one of them is looking decidedly unimpressed, so I ask what he made of the new minister. He pulls a gloomy face. "This isn't a real meeting, is it? It's just tea and biscuits." Then he cracks a knowing grin. "I mean, if he's sold his own party supporters down the river for a bit of power, he's hardly going to help us, is he?"

When I put the comment to Cable afterwards, he says, "Well people want to have it both ways, don't they? You can't win with some people. If you're not in government, you're criticised for being not serious. If you are in government, you're criticised for wanting power. That's the Labour party's line of attack, and it's a bit ridiculous."

But it's not just Labour's line. Almost everyone I know who voted Lib Dem has been saying more or less the same thing; that Cable's party has traded its principles for a taste of power, and betrayed its supporters. For once, Cable's mild, almost donnish manner vanishes.

"Well we haven't traded in principles for power," he objects. "We've got principles we've tried to inject into the coalition's thinking. The whole civil liberties agenda has changed out of all recognition. The idea that you'd have a Conservative party in government actually liberalising civil liberties is something that most liberal-minded people would have found very difficult to get their heads around. That partly reflects Cameron's instincts," he concedes. "But a large part of it reflects our influence."

"And on tax policy," he continues forcefully, "the Tory government on its own would never have dreamed of doing some of the things that appeared in the budget. You know, not a great deal of credit's been given but some very big changes have taken place. This idea of lifting the tax threshold is something I've fought for years in our party to get accepted, and it's a very big thing if you're a low-paid worker. Getting the bank levy through, getting the pension properly indexed. The capital gains tax we had a major battle over, and OK, we got a compromise." If the party has failed to get this message across so far, he sees it "as an issue of communication rather than a failure of strategy".

Could the coalition survive the failure of legislation for a referendum on AV? "Well we're not thinking about failure, so it's a double hypothetical. We're working on the assumption that the referendum will go ahead. We don't have a plan B, there's no reason to assume it won't." Nor, he says, is he worried about his party's post-election slump in the polls. "No, because I've been there before. When I was adopted as the Lib Dem candidate for Twickenham in 1989, we were on 3%. So no, I don't worry about it."

Cable could be forgiven for worrying. In the worst-case scenario, a year from now his party will have taken the flak for Tory cuts, been abandoned by its supporters in disgust, and lost the campaign for AV. If the coalition fails to deliver electoral reform, I wonder if Cable would feel his party's extraordinary experiment will have been worth it. "I think," he says firmly, "it would still be worth it."

At 67, Cable has waited a very long time to embark on a ministerial career. After such a long wait, it must be strange to stand accused of selling out in return for a taste of power. Would he say he's having more fun now than at any point in his political career?

"No, I wouldn't say that," he smiles. "It's more fun being in opposition. This is more satisfying than most of the other things I've done. But no, if you're looking for fun, it's better to be in opposition."