There is a whiteboard on the wall in Labour MP Dan Jarvis’s surprisingly spacious office at Westminster, with a series of bullet points under the headline “Radicalism and Realism”. I only see it when I’m leaving, although I’ve heard the slogan quite a few times in the course of the previous couple of hours. The subjects highlighted are fairly standard fare: a new political economy that is pro-business and pro-worker; a more federal UK; a new model welfare state; harnessing the digital revolution; managing immigration. The real question is why they are there. I’m sure this hasn’t been done for my benefit, and that it is the beginning of a manifesto – the manifesto of a man who would one day like to be Labour leader.

We meet at the end of what has been dubbed the longest reshuffle in history. “Well, that was quite a week,” says the shadow leader of the house, Chris Bryant, to Jarvis later as we are leaving the building. Jarvis laughs. Bryant has kept his job; Jarvis had no job to keep – he was a shadow justice minister in Ed Miliband’s team but has been ignored by Jeremy Corbyn. “Jeremy and I are not on each other’s speed dials,” he says wryly. It’s no secret he doesn’t share Corbyn’s uncompromising leftwing politics, but says he would serve under him if offered a suitable role.

Jarvis shares Bryant’s view that it has been quite a week. “I sat watching the 10 o’clock news and the first item was the fallout from the Labour reshuffle. The second item was North Korea testing a hydrogen bomb. Now you can blame the media for going on the reshuffle and not on the weapons test, but the reality is we have created an interest in ourselves that is not entirely helpful.” He is very fond of that euphemism.

He tweeted his support for fellow Barnsley MP and Corbyn critic Michael Dugher, who was sacked as shadow culture secretary. Was that a shot across Corbyn’s bows? “No, it was a reflection of sadness that people like Michael Dugher and Pat McFadden [who was sacked as shadow Europe minister] were not serving at the top table, because that’s where they should be.” He also dismisses the accusation from the shadow chancellor, John McDonnell, that the three ministers who resigned in protest at the reshuffle were members of a rightwing clique. “These are all serious, good people who’ve got a big contribution to make,” he insists.

Jarvis is not enamoured of the current state of the party. He says it’s in a state of “collective amnesia”. “We’ve lost two general elections on the trot, we’re on a downward trajectory as a party and have been for 10 or more years, and we need to understand why the public didn’t feel they could put their trust in us. We are an industrial party in a post-industrial age. If Clement Attlee turned up to a Labour party meeting tonight, he would feel very comfortable. The model by which we do our politics is outdated.”

He says the fact Labour has failed to renew itself since the mid-1990s largely accounts for Corbyn’s success. He was the one leadership candidate willing to be bold in his prescriptions. “The other three contenders were all good people, but none of them was saying anything that resonated with our membership. They represented more of the same, whereas Jeremy represented something quite different.”

Jarvis is a backbench MP, elected at a byelection in Barnsley Central in 2011. Normally, the thoughts of a relatively new backbencher on the state of his party would be of only passing interest, but what makes Jarvis’s views more intriguing is that he is second favourite, after Hilary Benn, to be the next leader of the Labour party. If Jeremy Corbyn fell under a bus tomorrow, Jarvis would have a good chance of succeeding him.

He came very close to standing last time, but in the end decided not to for family reasons – he remarried in 2013 following the death of his first wife from cancer three years earlier, and he and his second wife have a young daughter, as well as two children by his first marriage. Does he now regret having spurned the opportunity? “I’m not a great one for regretting anything,” he says. “But what I do regret is that I didn’t give it more thought beforehand.” He says he was working too hard for a Labour victory in the general election to ponder the consequences of defeat.

Miliband’s rapid exit took everyone by surprise. “I had 24 hours to make a decision. There was overwhelming pressure from members of the public, members of the party, colleagues in parliament for me to stand. They were asking me, in some cases instructing me, to do it, but, for the reasons I set out at the time, I didn’t.” He reckons Miliband jumped too soon. “It would have been helpful, not just to me but to a lot of people, if there had been a period of reflection through to the party conference. It would have been better if he had let the dust settle.”

Facebook Twitter Pinterest Jarvis during his time in the Parachute Regiment. Photograph: Labour party/PA

But Jarvis’s backers haven’t gone away, and he has recently taken on two political advisers, paid for by party donors, to help him develop a strategy. There are prominent Labourites who think he would have a far better chance than Corbyn of developing broad-based support for the party. Their faith derives from his backstory: a former paratrooper who served in Kosovo, Sierra Leone, Iraq and Afghanistan, rose to the rank of major, and became the first serving officer since the second world war to resign his commission to become an MP. Add the fact that when he won the Barnsley byelection, he had only recently lost his wife to cancer and was bringing up their two young children alone, and you have a character who, in an age dominated by Westminster clones, is seen as having that all-important hinterland.

He is also disconcertingly normal, which may or may not be an advantage. Born in Nottingham, the son of a Labour-supporting lecturer and a probation officer; educated at a local comprehensive; studied international politics at Aberystwyth University; went to Sandhurst but doesn’t have that standard army-officer public-school voice – if anything his accent is slightly West Country, picked up in the years he was stationed in Salisbury; classless, easy-going, nice – which he says you are taught to be in the army.

A colleague once described him as “bright in an army way”, which is a double-edged compliment, and you can see what he means. But David Cameron, despite his much-vaunted first from Oxford, is hardly an intellectual. Jarvis has that Blair saleability, the mien of a footballer and untameable hair, and if he did make it to PM he would at least look the part in a flak jacket or astride a tank.

A good backstory and personable manner can, however, only get you so far, and at some point you have to articulate a political vision. His critics have accused him of being “all things to all people” and “having no settled politics” – the attributes of a careerist. When I put that to him, he points to his support for the government in the crucial vote last month over military action in Syria. “If I had been this great political Machiavelli, plotting away and planning to be leader, I would have abstained or voted against military action,” he says. “But the guiding principle throughout my life is that you’ve got to do the right thing, and having looked at the evidence, my judgment was that the right thing to do was to vote in favour, which didn’t win me any friends with the leadership.”

There is, though, some truth in the suggestion that he doesn’t want to be identified with any of the factions within the party. “I delight in frustrating people’s desire to pigeonhole me,” he says. It is at this point that he first mentions “radical realism”. “We need fundamental change in the country, but we’ve got to keep it real. There are constrained resources, and it’s not credible to make promises if we can’t demonstrate how we will pay for them. But that doesn’t place me on the left or the right. I want to draw out the best of both wings of the party.”

One issue that can’t be fudged is unilateralism. This week’s reshuffle was essentially about Corbyn ending the split over Trident, which is why Maria Eagle, who favours renewing the nuclear deterrent, has been shipped into the calmer waters of culture, taking over Dugher’s former job. Emily Thornberry, who opposes Trident, will now be responsible for Labour’s policy on defence. Where does that leave the former paratrooper? “I am in no doubt that it is in our country’s national interest to renew Trident,” he says. “I’m not wild about the fact that as a country we’ll be spending billions of pounds doing that, but in terms of our security and our standing in the world, I am persuaded it’s the right thing to do.”

So how will he and the party negotiate the issue given that the leadership believes the opposite? “That is a fascinating dilemma,” he says. “I do have a specific concern about the [defence] review [being conducted by the party]. I was much more comfortable with it being led by two people [Eagle and Ken Livingstone] who had different views. That gave it balance. We’ve lost that, which potentially weakens and undermines the process. For it to have any credibility, it needs to be seen to be open-minded.”

Would he be willing to go into the next election on a unilateralist manifesto? “I couldn’t vote for it,” he parries, “and my advice would be not to go into it.” But if Labour conference ultimately backs scrapping Trident, would he fight on that ticket? “That’s a big question. To my core I have always been Labour and always will be, but I would feel deeply uncomfortable fighting as a Labour candidate on a manifesto that committed us to getting rid of our nuclear deterrent, not least because we would lose the election. It’s an issue of such strategic importance with the public that it would be catastrophic for us to go into an election with that as our policy.”

Facebook Twitter Pinterest Campaigning with Ed Miliband in the 2011 Barnsley Central byelection. Photograph: Peter Byrne/PA

If his advice to keep Trident is ignored, what will he do? “God knows. That is fortunately somewhere in the future. There’ll be quite a lot of water under the bridge before we get to that point.” Will there be a lot of leaders under the bridge, too? “Who knows?” he says. “There was an interesting question put to Diane Abbott yesterday, that if the review finds that it is in our country’s interest to renew Trident, then what does Jeremy do?”

I ask him whether the party could split on the issue. “I don’t think so,” he says. “That would be the road to nowhere, and I don’t detect any appetite for it. I’ve not heard anyone express in a serious way a desire to do that.” So what is the mood in the parliamentary Labour party? “People are understandably concerned about our direction of travel, but there will be electoral opportunities for us if we can sort ourselves out.” He reckons the divisions that will be exposed in the Conservative party by the EU referendum, which he expects in June this year, and a new, less “shiny” Tory leader will give Labour a chance in 2020 if the party can get its act together.

Does that mean Labour dropping the pilot? Here, Jarvis does equivocate. “Jeremy has got a big mandate from the membership. Many people were excited by the approach he took in the early days after his election. People wanted a kinder politics. The challenge is where the rubber hits the road – the day-to-day grind of parliament and being able to demonstrate that the kinder politics endures. The straight-talking model of politics has taken a bit of a hit in recent times.”

I return to the hypothetical bus, probably a number 73 heading up to Islington. If Jeremy did fall under it, would I be right in thinking the parliamentary party would not consider it the end of the world? “We are in the votes business,” Jarvis replies elliptically. “Politics is a very competitive process. At the moment, our opponents are better at this than we are. The Tory machine is a ruthless one. They are seeking to put us out of business, and they are making reasonable progress at it. People will be looking very carefully at the results of this year’s local elections.” I interpret this as code for if Labour does badly in May, then an anti-Corbyn bandwagon might start to roll, but Jarvis is wary of predicting an early change of leader. “There might be a few rogue bus drivers out there,” he says, “but I think Jeremy is pretty canny on that bike.”

Could a plot by the anti-Corbynistas be hatched? “Parliament has changed over the years,” says Jarvis. “I’ve been talking to people who were here in the 1960s and 70s, and in those days MPs talked to each other much more.” They were at Westminster late into the evening, would talk to each other in the tearoom or the bar, and out of that, conspiracies might form. Coups are much harder to mount – I should make it clear that he is talking entirely theoretically – when MPs are sitting in their offices in front of computer screens, not least because of the danger of the “reply all” button. A coup by email is unlikely, so for Corbyn’s critics in the parliamentary party it remains a case of waiting for something to turn up. Jarvis says he will continue to be guided by the motto of the Parachute Regiment, in which he served for 15 years: “Utrinque Paratus” – “Ready for anything”.

He is widely seen as the leader the Tories fear most. Portraying a former major who has fought in several war zones as weak would not be easy. But is that an encouragement or a millstone? “It creates a pressure and a tension that is not particularly helpful,” he says. “I could do without the target on my back.” People who desperately want to be leader – let’s call it the Heseltine syndrome – rarely get their wish, and Jarvis questions his rumbustious parliamentary colleague Jess Phillips’ willingness to talk about being a leadership candidate. “She’s a good mate and a breath of fresh air in this place,” he says, “but maybe she has a certainty about the future that I don’t have.”

A denial of sorts – but then, immediately, what I interpret as a countervailing statement of intent. “The world is a different place from last May. It may be less than a year, but it feels like a lifetime, and I’ve learned a lot about politics and the Labour party and the way we do things. For me the challenge now is to find a way that I can make a contribution.” Watch out for those buses, Jeremy.