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Jeremy Corbyn challenges Theresa May over the government's housing plans - criticising the cost of starter homes. Theresa May hits back with an attack on Labour's record in power and defends the Tories' record.

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Time now for Theresa May to cross swords with Jeremy Corbyn across the despatch box. The Labour leader begins by congratulating her on her appointment, noting she is the UK's second female prime minister.

He refers to her Downing Street statement which focused on tackling social injustice. He calls on her to proceed with a full public inquiry into the "terrible events at Orgreave".

Mrs May thanks him for his congratulations. She says she's long heard Labour asking what the Tories do for women - she says they "keep making us prime minister". She says she looks forward to the exchanges they will be having - and, to laughter says she hopes they'll continue for "many years to come".

On his question, she says the home secretary will be responding to an urgent question on the Orgreave inquiry after this session.

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Theresa May's first question comes from her own side - Conservative MP John Glen - who "warmly" welcomes her to her place. He asks Mrs May if she welcomes Monday's vote in the Commons in favour of Trident renewal.

The prime minister says she does - saying it showed that "we have not only committed to our own national security" but also Nato's. She says Trident renewal is "essential" and thanks the 140 Labour MPs who voted to support Trident - even though their leader's opposed.

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BBC deputy political editor John Pienaar says we should expect PMQs with Theresa May to be "very different from anything we've seen under David Cameron".

We've seen the "rapier" before but now we can expect the "mace and chain", he tells the Daily Politics.

And, as the party leaders face off in the Commons, Jeremy Corbyn's "leadership is on the line" while Theresa May's "couldn't be more secure".

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It's noon, it's Wednesday, which means one thing: it's Prime Minister's Questions time - and Theresa May is making her debut. She begins with supportive cheers from her backbenches, and with the customary statement, listing her official engagements for the day. She also welcomes today's employment figures.

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Several MPs, including the new Secretary of State, have paid tribute to the former Northern Ireland secretary Theresa Villiers, who stood down following Theresa May's appointment of her new Cabinet.

New Northern Ireland Secretary James Brokenshire says Ms Villiers has "played a very important role and made significant  contribution" in her last role.

DUP spokesman Nigel Dodds tells MPs Ms Villiers played an "enormously positive and constructive role in Northern Ireland" and was "instrumental" in the Fresh Start , externaland Stormont House agreements, external.

Northern Ireland owes an "enormous debt of gratitude to her", he adds. 

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Labour MP Cat Smith, who supports Jeremy Corbyn, says "we are not holding the government to account" in Parliament at the moment.

However, Labour needs to come together to make that happen, she argues.

Owen Smith supporter Chris Bryant, who has quit the front bench, claimed he "desperately wanted to make it work" but claims Mr Corbyn "never crafts a team".

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Labour MP Cat Smith says "as a democrat" she accepts the vote to leave the EU.

She tells the Daily Politics that the referendum was "fought on issues around immigration and that's the conversation we should be having".

Her constituents in Lancaster and Fleetwood have concerns about job security, she says.

"I don’t think the number [of immigrants] itself is important," she adds. "People need to know their jobs are secure," she argues, while the UK needs enough people to ensure, for example, that the NHS is staffed.

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The north-south interconnector would connect the two power grids by 138km of overhead lines between Moy in County Tyrone and County Meath.  

The project, which will take three years to complete, was meant to have been ready by 2017, but has been beset by delays.   

A public inquiry into the Northern Ireland part of the £204m cross-border energy project was launched in 2012 after a four-year delay in the project. 

Northern Ireland's Utility Regulator has said the cross-border link must be in place by 2019 "to keep the lights on and prices low".  

In the Republic of Ireland, the state-owned commercial energy company, EirGrid, has submitted plans for the southern half of the project.

In Northern Ireland, the lead is being taken by System Operator for Northern Ireland (SONI).

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Conservative MP Gavin Barwell insists the government will continue to "keep spending budgets under review" and deficit reduction is still a priority.

"We're not in a position where we can start spending money that isn't funded," he tells the Daily Politics.

However, there has been "very significant real-terms injection of money into the NHS" approved when George Osborne was Chancellor, he adds.

And will the NHS have sufficient staff, including migrants to the UK?

Mr Barwell says "we fully expect" EU citizens that are in the UK to be able to stay "but we also have British citizens that are in other EU countries". He hopes to secure the rights of both.

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DUP's David Simpson welcomes new Northern Ireland Secretary James Brokenshire to his post, and asks him to criticise the Irish Republican party Sinn Fein, as "one of the biggest objectors" to the 138km of overhead north-south electricity interconnector between County Meath and a new substation near Moy in County Tyrone.

Doesn't this show a "lack of understanding of simple economics"? Mr Simpson asks.

Mr Brokenshire replies that decisions over the project are devolved to the Northern Ireland Assembly but says he hopes "proposals can progress quickly" as they will have "significant potential to reduce costs".