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Yvette Cooper says she is "obviously disappointed" about coming third in the election but acknowledges Jeremy Corbyn's victory was "very strong". She says she expects him to now "reach out across the country to the public" after three months of internal debate. As to her own future, she says she does "not expect" to feature in the shadow cabinet but insists she will not "take her bat and ball home" and wants to play a leading role in campaigning for the UK to stay in the European Union.

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There's now quite a lot of focus on who will be taking roles in Jeremy Corbyn's top team. Asked whether he would remain as shadow defence secretary Vernon Coaker says:

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Green Party leader Natalie Bennett has said she and Jeremy Corbyn are united in their opposition to austerity, Trident and privatisation and says she wants to work with him on other issues, such as electoral reform. 

She adds: 

Here is the new deputy leader's acceptance speech

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Scotland's First Minister and SNP leader Nicola Sturgeon has congratulated Jeremy Corbyn on his victory and said she wants "to work constructively with him in a progressive alliance against Tory austerity".

But she has added:

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Andy Burnham tells BBC Radio 5 Live's chief political correspondent John Pienaar:

Asked whether he would resign his role as shadow health secretary, he said:

The New Statesman's Helen Lewis tells BBC Radio 4 that Corbyn's first challenge will be PMQs on Wednesday: "Will Labour MPs cheer him on or will there be a deathly silence?"

Jeremy Corbyn called for major changes to housing and welfare policies to help Londoners - to the delight of mayoral candidate Sadiq Khan.

Jeremy Corbyn and Tom Watson pose for pictures, as Fleet Street's best all vye to get that all important shot. 

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BBC assistant political editor Norman Smith says the outcome of the contest is "absolutely amazing". What is politically important is that Jeremy Corbyn won in every section so he has a "massive" mandate, Norman says. And for those who say he'll be gone by next summer they now have to tread "very carefully". Tom Watson, the new deputy leader, will be essential in keeping the show on the road, adds Norman.

"We go forward now as a movement and a party bigger than we been for," says Jeremy Corbyn in his final remarks. He says Labour is stronger and more determined than it has been for a long time - and will become more inclusive, involved and democractic, and "shape the future of everyone in this country". "Things can, and they will, change." he concludes - as people in the hall rise to their feet.

The Conservatives have used the 2008 economic crisis to impose a "terrible burden" on the poorest in society, claims Jeremy Corbyn. Labour needs an economic strategy that improves people's lives, expands the economy and reaches out to care for everybody, he tells the assembled crowd. He pledges more action to address inequality.

Back to the government's Trade Union Bill, Jeremy Corbyn says Labour will oppose it - as well as planned welfare reforms. His remarks now touch on the refugee and migrant crisis, saying the UK should respond with humanity, support and compassion. "We must recognise that going to war creates a legacy of bitterness and problems", Mr Corbyn says, adding:

"Let us be a force for change, humanity and peace in the world. "We are one world," he adds.