Video report by ITV News Political Editor Robert Peston
The Labour leader said his manifesto - titled "It's time for real change" - was full of popular policies that the political establishment had "blocked for decades".
"Over the next three weeks they will tell you that everything in this manifesto is impossible because they do not want real change in this country," he said.
He said the system was "rigged in their favour - but it's not working for you".
They know that Labour will go after the tax dodgers, the bad bosses and the big polluters, he said, as he unveiled a raft of major spending and taxation pledges.
Those pledges were were described by the Institute for Fiscal Studies think-tank as "colossal" and "not credible".
Mr Corbyn also accused Boris Johnson of using Brexit as "Thatcherism on steroids" as he sells off the NHS as part of the US trade deal.
In front of hundreds of supporters and with his Labour shadow front bench team behind him, Mr Corbyn outlined how his government would seek to rebalance society, making it fairer for all.
He said: "One third of Britain's billionaires donated to the Conservatives - the billionaires, the super-rich, the tax dodgers, the bad bosses, the big polluters, they own the Conservative Party ... but they don't own us."
He promised to nationalise the major sectors of rail, mail, water and energy.
Corbyn accepts 'hostility'
He continued his attack on the establishment by saying he expected hostility to his proposals.
"I accept the opposition of the billionaires, because we will make those at the top pay their fair share of tax to help fund world class public services for you – that’s real change," he said.
"I accept the hostility of the bad bosses paying poverty pay because we will give Britain a pay rise starting with a real living wage of at least £10 an hour, including for young workers – that’s real change.
"I accept the implacable opposition of the dodgy landlords because we will build a million homes, empower tenants and control rents – that’s real change.
"I accept the hostility of the big polluters because we will make sure they pay their fair share of the costs of their destruction, create a million climate jobs and build the healthy, green economy of the future – that’s real change.
"I accept the fierce opposition of the giant healthcare corporations because we will stop them sucking out profits from our NHS – that’s real change."
ITV News Business Editor Joel Hills takes a look at Labour's spending plans
'Not for sale, not for sale'
He told supporters the policies were fully costed with no increases in VAT or income tax or National Insurance for anyone earning less than £80,000.
He said that meant no tax increases for 95% of taxpayers.
On Brexit, Mr Corbyn once again accused the Tories of being ready to sell off the NHS to secure a trade deal with Donald Trump.
"Boris Johnson is trying to hijack Brexit to sell out our NHS and sell out working people," he said.
His warning prompted cries from the audience of "Not for sale, not for sale".
"The Conservatives want to use Brexit to unleash Thatcherism on steroids, to inflict more pain on the very communities so viciously attacked by Margaret Thatcher’s government in the 1980s, to benefit the billionaires and the vested interests they represent.
"That’s why Johnson is preparing to sell out our NHS for a US trade deal that will drive up the cost of medicines and lead to the runaway privatisation of our health service.
"£500 million a week of NHS money - enough for 20,000 new nurses - could be handed to big drugs companies as part of a deal now being plotted in secret."
Brexit 'done in six months'
Labour, he said, would deliver a new Brexit deal within six months - and put it to the people to decide on the future relationship with Europe.
"So if you want to leave without trashing our economy or selling out our NHS, you’ll be able to vote for it," he said.
"If you want to remain, you’ll be able to vote for that.
"Let’s take this out of the hands of politicians and give the British people the final say.
"It’s time to bring a divided country together so we can get on with delivering the real change Britain needs."
A green revolution - funded by windfall tax on oil & gas firms
On climate change, he said a Labour government recognised the emergency and as such would look to tax oil and gas companies "that profit from heating up our planet" who will shoulder the burden and pay their fair share through a Just Transition Tax.
"North Sea oil and gas workers have powered this country for decades, often working under dangerous conditions. We won’t hang them out to dry," he said.
"This fund will safeguard a future for their skills and communities with new careers and secure, well-paid jobs."
An investment blitz
Mr Corbyn said his government would "unleash a record investment blitz", with the aim of "breathing new life into your area".
"Our investment blitz will upgrade our national infrastructure in every region and nation, and rebuild our schools, hospitals, care homes and housing.
"Investment on a scale you have never known in every town, city and region," he vowed.
"Labour will transform our economy so that no one is held back, and no community is neglected."
On the side of the 'common people'
He stressed that Labour was on "your side", whether you're a student, nurse, pensioner or worker.
"If you’re a student, Labour is on your side. We’ll create a National Education Service, make lifelong education a right, value technical education as highly as academic learning and we’ll bring back maintenance grants and, yes, scrap university tuition fees.
"If you’re reaching old age, Labour is on your side. We’ll protect pensions and provide free personal care. If you’re living with a disability, Labour is on your side. We’ll update the Equality Act and scrap Universal Credit."
Labour's manifesto falls short of committing to support the continuation of freedom of movement if the UK leaves the EU.
It does commit the party to creating "a humane immigration system" and says the 2014 Immigration Act would be scrapped under a Labour government.
It also confirms that EU nationals will be granted the automatic right to continue living and working in the UK under a new "declaratory system".
Labour's manifesto makes clear that freedom of movement would continue if the UK remains part of the EU, but adds that the situation will be "subject to negotiations" if Brexit takes place.
ITV News Political Editor Robert Peston quizzes Mr Corbyn on the detail of nationalising industries and potentially staying in the EU
In conclusion, Mr Corbyn insisted the chance was there for a once-in-a-generation change and believed the British electorate was ready to support his vision.
"Ignore the wealthy and powerful who tell you that’s not possible," he said. "The future is ours to make, together."
"As the writer Pablo Neruda wrote so beautifully: 'You can cut all the flowers but you cannot keep Spring from coming.'
"Vote for this manifesto of hope. It’s time for real change."
Reaction - "these are vast numbers, colossal"
Paul Johnson, head of the independent think-tank the Institute for Fiscal Studies, was stunned by the figures being quoted in the Labour manifesto.
He told ITV News Political Correspondent Daniel Hewitt that “it’s impossible to overstate just how extraordinary this manifesto in terms of the sheer scale of money being spent and raised through the tax system”.
Mr Johnson said: "Hundreds of billions of additional spending on investment, £80 billion plus per year on spending on day-to-day things; social security, spending on the NHS, students loans and so on. Matched by, supposedly, an £80 billion increase in tax.
"Now you can talk about tens, hundreds of billions of pounds... take it from me, these are vast numbers - enormous, colossal, in the context of anything we’ve seen in the last...ever...really.”
The IFS director said it was "simply not credible" to expect Labour to raise £80bn of tax revenue all from companies and people earning over £80,000 a year.
"You cannot raise that kind of money in our tax system without affecting individuals," said Mr Johnson.
Conservative party want questions answered
While Boris Johnson dismissed the Labour manifesto as having no "economic credibility" due to the party's stance on Brexit.
The Prime Minister said: "What we want to know is what is his plan to deliver Brexit and what's the deal he wants to do and which side would he vote on that deal and we still don't know.
"Until we have answers to those questions, until we get Brexit done, none of this carries any economic credibility whatever."
See the full Labour Party manifesto here:
And you can look at the numbers behind it for yourself, here: