Jeremy Corbyn has set out his election stall by promising “21st century socialism” for Britain, taxing the super-rich, pouring borrowed money into new council houses and blocking arms sales to abusive regimes.

Mr Corbyn told the Labour conference in Liverpool the only way his party can win the next election – a task he said was a “mountain to climb” – would be to follow the left-wing agenda he has always wanted to pursue.

The speech, his first major set-piece since winning a second leadership contest, showed Mr Corbyn now feels he has authority to push ahead with his plans.

In a move symbolising his direction he said he would lift a cap on councils wanting to borrow money to build homes, he promised rises in corporation tax to pay for education and a foreign policy that focused on human rights and peace.

He moved quickly over the political turmoil of the summer, urging all in the party to end the “trench warfare” that has come to characterise Labour in recent months, and warning of failure if they fail to unite.

The speech revealed a bolder, more confident and polished leader than the one who stumbled through a speech at conference in 2015.

On that occasion the North Islington MP, unused to reading from an autocue, said the stage direction “pause” out loud by mistake. But in Liverpool he was introduced as “your socialist leader” and came across relaxed and even able to deliver a convincing joke.

In a nod to the so-called "Traingate" scandal he told delegates Virgin trains had been in touch to assure him there were 800 empty seats in the packed hall in front of him.

Having broken the ice, he then told delegates: “We know how great this country could be, for all its people, with a new political and economic settlement.

“With new forms of democratic public ownership, driven by investment in the technology and industries of the future, with decent jobs, education and housing for all with local services run by and for people not outsourced to faceless corporations. That’s not backward-looking, it’s the very opposite. It’s the socialism of the 21st century.”

He said it was now the job of Labour to “win over the unconvinced to our vision” adding, it's the “only that way can we secure the Labour government we need.”

It followed a difficult conference in which divisions were sometimes embarrassingly exposed between his camp and that of moderate MPs who quit his frontbench in the coup of the summer.

Snubbing his detractors, he instead praised those backbenchers who had stepped up when frontbench positions came free following the revolt, as some of the rebels clapped politely in the wings.

He went on: "And let’s be frank, no one will be convinced of a vision, promoted by a divided party. We all agree on that. So I ask each and every one of you, accept the decision of the members end the trench warfare and work together to take on the Tories."

Mr Corbyn acknowledged the big challenge ahead if Labour is to return to power, saying: “It’s true there’s an electoral mountain to climb.”

But he argued that delivering socialism for the 21st century was the key, making three key pledges – the first on housing. He condemned the lowest level of housebuilding since the 1920s, falling home ownership, rising evictions and homelessness, and the sale of council homes without replacements.

The leader said: “Another consequence is that we’re paying over £9bn a year to private landlords in housing benefit. Instead of spending public money on building council housing, we’re subsidising private landlords. That’s wasteful, inefficient, and poor government.

“So, today, I’m announcing that Labour will remove the artificial local borrowing cap and allow councils to borrow against their housing stock. That single measure alone would allow them to build an extra 12,000 council homes a year.”

In another key pillar of his socialist platform Mr Corbyn promised a high-quality National Education Service, to deliver for a nation “rich in talent, rich in potential”.

Labour’s National Education Service is going to be every bit as vital as our National Health Service has become <p>Labour leader, Jeremy Corbyn</p>

He contrasted that with a Conservative government that had “slashed adult education budgets, taking away opportunities for people to develop their skills and leaving businesses struggling to find the skilled workforce they need”.

The solution was a “new deal for rebuilding Britain”, he said, with a corporation tax rise of “less than 1.5 per cent” to bring back an education maintenance allowance for college students and grants for university students.

Directly addressing business leaders he said: “We will ask you pay a little more in tax. Business shares in economic success and it must contribute to it too.

“Labour’s National Education Service is going to be every bit as vital as our National Health Service has become.”

All school pupils would also have “the chance to learn an instrument take part in drama and dance and have regular access to a theatre, gallery or museum in their local area”, through a £160m programme.

Today Jeremy talked about Labour getting ready for, and winning, the next election. After a largely wasted year for the party that's what the country needed to hear <p>Unison general secretary, Dave Prentis</p>

Hitting out at the wealthiest in society, he said: “Government might be a bit more efficient if the super-rich like Sir Phillip [Green] actually paid their taxes. When government steps back there are consequences for every one of us.”

Perhaps closest to the emboldened leader’s heart were his positions on foreign policy, which he has spoken out on in the Commons for decades.

Mr Corbyn promised no repeat of the “disastrous” wars in Iraq and Libya – blaming them for “the spread of terrorism, sectarianism and violence”, as well as the refugee crisis.

In a move likely to anger moderates, he said: “We have to face the role that repeated military interventions by British governments have played in that crisis.”

Jeremy Corbyn criticised the continued sale of arms to Saudi Arabia (Getty Images)

Then to a standing ovation, he added: “That is why it was right to apologise on behalf of the party for the Iraq war, right to say that we have learned the lessons and right to say that such a catastrophe must never be allowed to happen again.”

The Labour leader then criticised the continued sale of arms to Saudi Arabia, “a country that the United Nations says is committing repeated violations of international humanitarian law war crimes in Yemen”.

He told the conference “So, today, I make it clear that under a Labour government, when there are credible reports of human rights abuses or war crimes being committed, British arms sales will be suspended, starting with Saudi Arabia.”

The speech won unlikely praise from arch-Corbyn critic John Woodcock, who previously branded his leader a “f***ing disaster”, who was turning the party into a “laughing stock”.

The backbench Barrow MP tweeted: “A well-delivered speech from Jeremy with a firm direction. Let's all do what we can to help tackle the 'electoral mountain' he identifies.”

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Stephen Kinnock, the Aberavon MP, said Mr Corbyn's speech was “very strong” on the economy but he questioned his position on immigration, largely unchanged from that which failed to convince voters at the last election.

He said: “My understanding is he is not of the view that we should be setting numbers and targets and I think we have to.”

Unison general secretary Dave Prentis said: “Today Jeremy talked about Labour getting ready for, and winning, the next election. After a largely wasted year for the party that's what the country needed to hear.

“We must ignore the doom-mongers, the next election is not lost, but the year ahead has to be about how Labour wins back the support of voters across the country.”

Adam Marshall, acting director-general of the British Chambers of Commerce, said businesses wanted investment in infrastructure and skills, but added: “Many will be concerned that Jeremy Corbyn is already reaching for the tax lever by asking businesses to pay for his education plans.

“As the Labour party develops its proposals further, it has to get the balance between these factors right – or risk denting business confidence and investment.”

Conservative Party chairman Sir Patrick McLoughlin said: “This conference has shown Labour are too divided, distracted and incompetent to build a country that works for everyone. They would spend, borrow and tax even more than they did last time, support unlimited immigration, and cannot be trusted to keep our country safe.”