Mr Corbyn, who represents the radical left, accused the Prime Minister of being a “poverty denier” in his address to the Trades Union Conference in which he insisted the government’s welfare reforms had cost lives.
He also branded proposed restrictions on strikes an attack on civil liberties and called for “solidarity” with workers around the world, blaming a “free market philosophy” for workplace tragedies in China.
The rallying call came after a tricky start to Mr Corbyn’s stewardship of the party following his overwhelming election victory. Many MPs, including frontbenchers, have signalled disquiet over the appointment of hardliner John McDonnell as shadow chancellor.
There are also complaints that none of the most senior jobs in his top team have gone to women.
The 20-minute quick-fire address to delegates in Brighton, delivered tieless, was originally intended to include a passage invoking Margaret Thatcher’s 1980s phrase to warn that the Conservatives still regard unions as “the enemy within”.
However, Mr Corbyn did not deliver the pre-briefed lines, with Labour officials saying he was working from notes and simply “forgot”.
Mr Corbyn said the TUC conference was a “shared celebration of our values as a Labour and trade union movement”.
“Values of solidarity, of compassion, of social justice, of fighting for the under-privileged, and for all working people at home and abroad. Those are the values that have shaped me and my political life,” he said.
He signalled that Labour would now oppose all the Tories welfare changes, including the benefit cap.
“Labour will oppose the Welfare Bill in full. We oppose the benefit cap. We oppose social cleansing,” he said.
“We will bring the welfare bill down by controlling rents and boosting wages, not by impoverishing families and socially cleansing our communities.”
The new Labour leader delivered an angry retort to jibes that he is a “deficit denier”.
“But then they spend billions cutting taxes for the richest families or for the most profitable businesses,” he said.
“What they are is poverty deniers – ignoring the growing queues at food banks, ignoring the growing housing crisis, cutting tax credits when child poverty rose by half a million under the last government to over four million.
“Let’s be clear – austerity is a political choice, not an economic necessity.”
Mr Corbyn received a rapturous welcome on arrival at the conference centre, and a standing ovation when he reached the stage.
Addressing delegates as “sisters and brothers”, he said trade unionism was “in my body”.
He stressed the importance of helping unions in other countries, saying workers should stand in solidarity with others across the world.
Referring to a major fire in the Chinese port of Tianjin last month which claimed more than 100 lives, Mr Corbyn said: “Those people that died in that dreadful fire in China, where there was a free market philosophy around the operation of the port, firefighters died trying to protect other workers who should have been protected by decent health and safety conditions.”
Mr Corbyn denied that trade unionism and “solidarity” were a “thing of the past”.
He said the Labour leadership contest had enthused thousands of people about the “way things could be done better”.
The number of people who voted for him was twice the membership of the Conservative Party, he said.
Some 30,000 people have joined Labour since the result was announced, he added.
Again hinting that the Labour conference could regain its policymaking powers, Mr Corbyn said he wanted to take a “different approach” and stop policy being set “top down” from the leadership.
“I want everybody to bring their views forward,” he said. “Every union branch, every party branch, every union.”
Mr Corbyn insisted he would not be “lectured” by figures suggesting Labour needed to “distance” itself from the unions to get elected.
He said if he became prime minister in 2020 he would repeal the Trades Union Bill and replace it with a “workers’ rights agenda”.
He said the measures would see civil servants trawling through social media to see if union officials were breaking rules, and amounted to an “attack on civil liberties”.
“Why shouldn’t workers organised together in a union express a political view?” he added.
“Why shouldn’t they use their funds, if they wish, on political or public campaigning? They seem quite relaxed about the involvement of hedge funds and funny money in politics, they seem absolutely obsessed with the cleanest money in politics, which is trade union funds being used for political campaigning.”
Mr Corbyn said the Welfare Bill was about “making the lives of the poorest and most vulnerable in society even worse”.
He said previous changes introducing new tests for the sick and disabled had “disastrous appalling consequences”.
“What kind of a society are we living in where we deliberately put regulations through knowing what the effects are going to be on very poor and very vulnerable people who end up committing suicide, and we say it all part of a normal process? No it is not,” he said.
Mr Corbyn insisted Labour’s job was to “set out a vision for a better society”.
“We are actually quite a rich country,” he said. “We are actually a country that is deeply unequal.”
The Islington North MP said the founders of the unions and of the Labour party had been determined to “do things differently”, and managed to extend the right to vote and to create the NHS.
“We build on that in the way we inspire people to come together for a more decent, more equal, fairer and more just society,” he added.
“These things are not dreams. These things are practical realities that we, together, intend to achieve.”
Unite general secretary Len McCluskey said Mr Corbyn was received with the same “warmth” as he experienced in his meetings around the country during his leadership campaign.
“It was incredibly refreshing to have a Labour leader embrace trade unions, as opposed to the Prime Minister who used to call us the enemy within,” he said.