The World at One
BBC Radio 4

The GMB union's general secretary, Sir Paul Kenny, says it's one thing to win an internal Labour election but there is "a massive task" ahead for the party to win back traditional voters and appeal to a broader ranger of new ones. Can Jeremy Corbyn do that? "The jury's out. We'll have to wait and see," he says. Mr Kenny says Mr Corbyn's first big test was the shadow cabinet "and let's see how that gels first". The appointments were interesting for both who was and was not included, he adds.

The Daily Politics

Stephen Kinnock, Labour MP for Aberavon and son of former party leader Lord Kinnock, has said Jeremy Corbyn must be willing to negotiate when it comes to policy on Trident. Mr Corbyn has previously said he would like to scrap the nuclear deterrent.

Speaking to the Daily Politics earlier, he said:

Here's the full list of people joining the new Labour leader's team.

Deputy leader: Tom Watson

Shadow first secretary of state and shadow business secretary: Angela Eagle

Shadow chancellor: John McDonnell

Shadow chief secretary to the Treasury: Seema Malhotra

Shadow home secretary: Andy Burnham

Shadow foreign secretary: Hilary Benn

Opposition chief whip: Rosie Winterton 

Shadow health secretary: Heidi Alexander

Shadow education secretary: Lucy Powell

Shadow work and pensions secretary: Owen Smith

Shadow defence secretary: Maria Eagle

Shadow Lord Chancellor and shadow justice secretary: Lord Falconer of Thoroton

Shadow communities and local government secretary, and shadow constitutional convention minister: Jon Trickett

Shadow energy and climate change secretary: Lisa Nandy

Shadow Commons leader: Chris Bryant

Shadow transport secretary: Lilian Greenwood

Shadow Northern Ireland secretary: Vernon Coaker

Shadow international development secretary: Diane Abbott

Shadow Scottish secretary: Ian Murray

Shadow Welsh secretary: Nia Griffith

Shadow environment minister: Kerry McCarthy

Shadow women and equalities minister: Kate Green

Shadow culture, media and sport secretary: Michael Dugher

Shadow minister for young people and voter registration: Gloria De Piero

Shadow mental health minister: Luciana Berger

Shadow Lords leader: Baroness Smith of Basildon

Lords chief whip: Lord Bassam of Brighton

Shadow Attorney General: Catherine McKinnell

Shadow Minister without Portfolio: Jonathan Ashworth

Shadow housing and planning minister: John Healey

Jeremy Corbyn has unveiled his complete shadow cabinet team - and we learn that Maria Eagle is to become the shadow defence secretary. Michael Dugher gets the shadow communities and local government brief, while work and pensions goes to Owen Smith.In a statement, the Labour leader said the line up was "unifying, dynamic and inclusive" - and for the first time "has a majority of women". In addition to the usual roles, he has established a position for mental health. Full list to follow.

The Daily Politics

New shadow international development secretary Diane Abbott says Jeremy Corbyn didn't have a lot of room for manoeuvre when it came to the top four jobs. She says the Labour leader was right to appoint John McDonnell as shadow chancellor, as he has the "fiercest commitment" to Mr Corbyn's central offer of being anti-austerity.

However Labour MP Diana Johnson says the role could have gone to Angela Eagle which would have been evidence of Mr Corbyn's promised "new style of politics" - as she would have been the first female shadow chancellor.

The Daily Politics

Proposed changes to trade union laws are under discussion on the Daily Politics. Cabinet Office minister Matt Hancock insists the Trade Union Bill is "a set of reasonable changes" to help make the economy work better. He says some unions can adopt "aggressive" and "bullying" tactics and that the bill will put the code of practice - "which is almost all of the time followed anyway" - on a statutory basis. He also rejects claims the proposals are "anti-democratic", pointing out that they were in the Conservative manifesto.

But PCS boss Mark Serwotka says industrial action is the "last resort" when talks have failed and is designed to put pressure on employers. He calls Mr Hancock a "hypocrite", saying he wants more people to vote but won't allow union members to vote in ballots online or by phone. Mr Hancock says it has not been ruled out. 

The Daily Politics

Public and Commercial Services (PCS) union general secretary Mark Serwotka confirms he was barred from voting in the Labour leadership election because, in the party's words, he didn't share its "aims and values".

"I found it extraordinary," he tells the Daily Politics, saying he is on "exactly the same page" as Jeremy Corbyn. He says the unions have "a lot to offer" Labour in policy development, welcoming Mr Corbyn's promise for a more collegiate approach. He adds that he agrees with John McDonnell's economic outlook, including on renationalisation.

Downing Street says the government has extended an invitation to Jeremy Corbyn to join the Privy Council, a formal group of advisers to the Queen.

The appointment of leaders of the opposition as Privy counsellors allows the government to share confidential information with them, including matters of national security.

Asked whether David Cameron would invite the new Labour leader to National Security Council briefings the prime minister's official spokeswoman said he'd "invited the leader of the opposition before and I'm sure he'll be open to that in the future".

She refused to say whether the government would insist on Mr Corbyn joining the Privy Council first.

BBC News Channel

Unison general secretary Dave Prentis - speaking from the TUC conference in Brighton - attacks the government's Trade Union Bill, due to be debated by MPs this afternoon as "vicious", "vindictive" and "Stalinist". "It will make the voice of workers absolutely neutered," adds Mr Prentis.

BBC News Channel

Former Labour London mayor Ken Livingstone defends John McDonnell’s appointment as shadow chancellor. Seeking to highlight his experience, he says he had “a real grasp of detail” when he was chair of finance at the Greater London Council, where he managed and balanced “massive” budgets. And he has “an answer for a way out of the mess we’re in”, he adds. Mr Livingstone – who says he hasn’t spoken to Mr Corbyn since his victory - adds a Labour leader has to have a chancellor he can trust and work with.

BBC News Channel

Is there a danger of a purge of moderate Labour MPs? "I don't give that much credence," says Chris Bryant. He says it's going to be "a bumpy ride" ahead and the party has "a lot of learning to do". But he adds:

BBC News Channel

Chris Bryant confirms he turned down the defence brief because "I disagree with Jeremy about quite a lot of defence issues", such as leaving Nato and his attitude towards the Middle East and Russia, he adds.

A pro-EU MP, he says after talking to the new Labour leader - who has appeared less committed to continued British membership - he felt "perfectly happy" on his position on the EU. 

It comes after ex-shadow business secretary Chuka Umunna said a lack of commitment from Mr Corbyn to the EU was his reason for quitting his position yesterday.

The Daily Politics

Jo Coburn is joined by journalist Steve Richards to discuss the election of Jeremy Corbyn as Labour leader, his new shadow cabinet and government plans to tighten rules on trade union strike ballots.

Her guests will include Toby Perkins, who managed Liz Kendall's leadership campaign, plus backbench reaction from MPs Stephen Kinnock and Diana Johnson.

Coburn will also talk to Mark Serwotka, the general secretary of the Public and Commercial Services Union, live from the TUC Congress in Brighton, and to Cabinet Office Minister Matt Hancock.

The Daily Politics is live on BBC Two from 12:00 to 13:00 BST, and online viewers - on mobile or desktop - can watch on the live coverage tab above. 

BBC News Channel

Asked about the high profile names refusing to serve under Jeremy Corbyn, Chris Bryant, shadow leader of the Commons, says he fully respects their choice but explains his decision to take a job in his team: "I felt in the end that the Labour Party has to unite." 

He says Labour threw its cards up in the air on Saturday and sent a message that it wants politics to be done in a different way. 

"The job I've got is all about how we do our politics in there (gesturing to Parliament)," he adds.