Jeremy Corbyn insisted he would put nuclear disarmament at the heart of his leadership re-election campaign as he promised to vote against the renewal of Trident in a Commons debate that will expose deep divisions within the Labour party.

In an interview with the Guardian at the Tolpuddle festival in Dorset, the party leader added that he would like Labour to switch to supporting unilateralism ahead of the motion that will likely cause MPs to split three ways on the future of the deterrent.

“I will be voting against continuous at-sea deterrent, because it rules out any compliance with the nuclear non-proliferation treaty,” he said. “I’ve been involved in peace transformation all of my life, and I think we’ve got an opportunity to show leadership in the world.”

He said that although party policy was formally pro-renewal, he hoped to reverse that over time and formally commit Labour to disposing of Britain’s nuclear weapons unilaterally. “I recognise people are going to take some time to get into that position [unilateralism], but I ask them to look at the world as it is,” he said.

His stance differs from that of his key allies Emily Thornberry and Clive Lewis, shadow foreign and defence secretaries respectively, who revealed in a Guardian article on Saturday that they will abstain in Monday’s vote. Many other Labour MPs, including Corbyn’s two challengers Owen Smith and Angela Eagle, say they will vote for renewal. Labour MPs have been given a free vote on the issue.

Corbyn said he would spend his leadership re-election campaign this summer taking his message to “left-behind Britain” and confidently predicted he would see off his challengers and go on to beat Theresa May in a general election.

Corbyn has been hit by scores of resignations and has failed to win the backing of 80% of his MPs in a confidence ballot since Britain voted to leave the European Union in June’s referendum. Two former members of the shadow cabinet, Eagle and Smith, launched challenges against his leadership last week.

Corbyn said: “My message is going to be, as well as having the debate within the party, let’s do some campaigning to reach out to the parts of left-behind Britain that often voted to leave the European Union, and in some cases have turned to Ukip.”

Asked if he could beat May, the new prime minister,in a general election, he said: “It’s not a presidential system. But could Labour win a general election? Yes. Could I lead Labour to win a general election victory? Yes of course, that’s why we’re here”.

Jeremy Corbyn marches in the Tolpuddle Martyr’s Rally in Dorset. Photograph: Geoff Moore/REX/Shutterstock

He added that May’s pledge in Downing Street last week to govern on behalf of struggling working-class families was the direct result of his taking over at the top of Labour. “That wouldn’t have happened if we hadn’t won the leadership last year. That debate simply would not be taking place. The whole economic debate has moved very much towards the left because of the work of those that supported our leadership campaign last year,” he said.

Corbyn will face May at prime minister’s questions in the House of Commons for the first time on Wednesday, and said he expected it to be a less jocular affair than under David Cameron.

“She’s very serious in her style, very well-informed in her style, it won’t be the same as David Cameron,” he said, welcoming the idea of a more sombre tone. “Parliament ends up like a theatre and a club, and it shouldn’t be.”

Corbyn appeared to single out Eagle as the more rightwing of his two rivals, claiming that as shadow business secretary, she was reluctant to support the idea of state involvement in rescuing the steel sector when the Port Talbot steelworks was put up for sale earlier this year.

“After a lot of discussion, we agreed a position on the steel industry, and Angela accepted the need for state intervention, to help the industry survive. She was less persuaded of state intervention in the beginning, but she did come round, and I welcome that.”

He was more conciliatory about Smith, the former shadow work and pensions secretary, saying: “Owen assured me he was not part of the wave of resignations – the plot – but sadly he resigned. I say to Owen, you’ve got talent, you’ve got ideas, you’ve got ability: get on board. Let’s work together.”

Smith and Eagle are expected to hold a hustings on Monday to determine which of them will stand against him as the “unity candidate”, while the party’s national executive committee will meet on Tuesday to decide to discuss the controversial framework for the contest, including a six month cut-off point for members to qualify to vote.

Earlier on Sunday, Smith and Eagle went head-to-head in a debate on BBC1’s Andrew Marr show, chatting with great courtesy but revealing significant differences over how to approach the impending battle with Corbyn.

Smith called for a swift party decision over which of the pair should challenge Corbyn and suggested that whichever of the pair won more nominations from Labour MPs and MEPs should be chosen. Eagle, who is believed to have fewer confirmed supporters than Smith, disagreed.

“I think one of us standing would be better, is the honest answer,” said Smith. “But I think the PLP (parliamentary Labour party) has got to be a grownup organisation and come to a decision in the next couple of days as to who it is.

“My view is, whoever is the person who commands the larger degree of support in the PLP is the unity candidate, and that’s the person who should go forward and take Jeremy on.”

Eagle disagreed, saying: “I think we have to have the person that’s most likely to beat Jeremy Corbyn, and I think that’s me.” Pressed by Marr how an agreement might work, she added: “We’re not going to do a deal here on your sofa, beautiful though it is.”

Eagle presented herself as the experienced, capable Labour voice, saying she had “wiped the floor” with George Osborne at prime minister’s questions, when they had deputised for their leaders. “I’m a working-class woman and that’s what we need at the moment,” she said.

A Jeremy Corbyn supporter at Tolpuddle Martyrs Rally in Dorset. Photograph: Geoff Moore/REX/Shutterstock

In his speech to a sympathetic audience in Tolpuddle – part festival, part political rally – where Keep Corbyn T shirts were scattered throughout the crowd, he said the protests that take place outside parliament help to influence the government’s decisions – claiming victory for the rejection of the tax credit cuts, for example.

He said Labour should be reaching out into rural areas. “Poverty can exist in a chocolate box village in the midst of beautiful countryside,” he said. “Devon and Cornwall have the lowest wage rates of the UK”.

He said he believed Labour could succeed in areas such as the south west, which were Liberal Democrat strongholds before the party collapsed at last year’s general election. “Labour has a very important message, but we only succeed if we reach out. It’s about economic justice, and it’s a message for the whole of the UK”.

Despite the ferocious tone of the battle for his party, he insisted he was “in absolutely fine fettle” and even joked about Cameron’s tribute to his cat at the outgoing prime minister’s final appearance in the Commons last week. “He did say some very nice things about my cat; I thought he was very nice about El Gato. I spoke to the cat when I got home and he was very pleased.”