Some key lines from the manifesto:

• Zero hours contracts will be banned to guarantee workers a "number of hours each week"
• Maximum pay ratios of 20:1 to be rolled out in public sector
• Four new public holidays to mark national patron saints' days
• Raise minimum wage to "at least £10 per hour by 2020"
• Ban unpaid internships
• "Clamp down on bogus self-employment" and extend rights of employees to all workers - including shared parental pay

The Labour leader answers questions, including one from the BBC's political editor Laura Kuenssberg.

Labour's draft manifesto (leaked last week) said:

  That’s changed to:  

Norman Smith
Assistant political editor

Jeremy Corbyn is pouring money at the electorate, but do people believe that is credible? That is the key question Labour is facing.

The party has put out a costing document, but what we don't know is how much more Labour would borrow. That's because the cost of buying back public utilities - massive, colossal sums of money -  none of those figures are in this document.

Labour's manifesto pledges to work with the Welsh Government to scrap tolls on the Severn Bridge between England and Wales.

Well, in the middle of the launch, what do you know, a policy announcement from the Conservatives.

In a press release apparently from Theresa May herself, we're told she will abolish tolls on Severn Crossings between Wales and England.

This, the announcement adds, will give a £100 million boost to the local economy. Coincidental timing. 

Jeremy Corbyn rules out VAT and national insurance rises, with a new minimum wage of £10 by 2020.

On rail renationalisation:

• The draft manifesto only mentioned taking control back when franchises expire
• Today’s adds that they could be taken back into public ownership “with franchise reviews or break clauses”

On rail operation:

• The draft manifesto said Labour would “ending driver only operation”
• This has been watered down to say they will now be “ending the expansion of driver only operations”

On Heathrow:

• The draft manifesto said Labour “supports expansion of aviation capacity”
• Today, this has been changed to “recognises the need for additional airport capacity” and puts in a host of caveats not mentioned in the draft, including:  Adherence to tests covering noise issues, air quality, and UK’s climate change obligations

Image source, Getty Images

"It's not a cult of personality, don't worry about it," says Jeremy Corbyn. That was in response to boos from some members of the audience to a question about his unpopularity as leader and the possibility that the manifesto is a throw back to the 1970s.

Dripping with sarcasm, the Labour leader goes on: "I simply say, the other party contesting this election is very forward-looking - they're going to bring back fox hunting and grammar schools. 

"Very 21st Century."

Press Association

According to the Press Association, Labour's shadow defence secretary has turned down an invitation to be at the party's manifesto launch.

Nia Griffith has disagreed with Jeremy Corbyn over support for the Trident nuclear weapons system.

PA says a source close to Ms Griffith confirmed she had been invited but wanted to be out campaigning in her Llanelli constituency.

Branwen Jeffreys
Education Editor

Increasing entitlement to childcare as set out in the Labour manifesto would cost an additional £5.3bn - this is based on research published last year by the Joseph Rowntree Trust on what an "anti poverty childcare system would look like".

The manifesto suggests moving away from a complex system of tax and benefit subsidies to parents and towards direct subsidies to childcare providers. 

There are plenty of questions though, including whether Labour intends to provide free childcare for even the wealthiest children - the Conservative promise of 30 hours free a week doesn't apply to families where one parent earns more than £100,000. 

Jeremy Corbyn is taking questions now and is asked about the degree of costing in the plans he has set out.

This manifesto is about rebalancing the economy, says Jeremy Corbyn. He says every other country wonders why Britain does so little about the "grotesque levels of inequality" - and that's what his programme aims to do. 

The creation of a national investment bank will help spread prosperity around the UK, he adds.

"Our manifesto offers hope," says Jeremy Corbyn, working up to his final flourish.

"Our manifesto is for the many, not the few." 

And with that, he's done, and so begins sustained applause from the appreciative audience.

"The Tory campaign is based on one word - fear," says Jeremy Corbyn. "Will the Tories change their spots? Don't count on it."

He says the prime minister "will disagree", adding: "So I say to her, 'Come out of hiding and let's have a debate'."

Mr Corbyn says he wants a "polite and respectful debate" on TV so people can make up their own mind.

The Labour leader has tried to persuade the PM to agree to just such a debate - including submitting a question to her Facebook Live ITV interview yesterday - but so far she's steadfastly resisted his appeals.

More cheering as Jeremy Corbyn sets out Labour's commitments to renationalising the railways and parts of the energy sector.

Moving onto Brexit, he says the British people voted to leave the EU so that is what a Labour government would do, but only a Labour government would protect jobs and single market access as it happens.

It seems the line we brought you earlier about taking foreign students out of immigration figures has been tightened up since last week's leak.

• Draft manifesto says intenational students make big contribution, “welcomes” them, but does not say it will take them out of migration figures
• Final document says: “They are not permanent residents and we will not include them in immigration numbers, but we will crack down on fake colleges.”

Jeremy Corbyn runs through some of Labour's biggest pledges. The biggest cheer from the audience comes when he says it will scrap tuition fees for university students. 

More social housing, more police officers, "a move towards universal free childcare", "ending hospital car parking charges" and "four extra public holidays each year".

Mr Corbyn says he recognises that "a thriving economy" is the only way to achieve all these things.

"Labour will unlock this country's potential," he insists.