Asked about the allegations about Labour MP Keith Vaz's private life, Theresa May says: "What Keith does is for Keith, and any decisions he wishes to make are for him. But I think that overall what people look for is confidence in their politicians."

In response to a question on immigration from the BBC's Laura Kuenssberg, Theresa May again repeats that the public want "an element of control" on the numbers coming to the UK - and that there are various ways to do that.

"We will be coming forward in due course with those proposals," she adds.

Pressed on the current immigration figures - which are way above the government's "tens of thousands" pledge - she says the numbers initially came down but have subsequently risen.

But she argues that by leaving the EU the UK will have the ability to control movement of people coming from EU in to UK which, she says, is not possible while being a member of the bloc.

Asked if she's gone soft on reducing immigration, after she ruled out an Australian points-based system advocated by Brexit campaigners during the referendum campaign, Mrs May shakes her head and says: "No."

She says the public, in voting to leave the EU, showed they wanted some control on immigration to the UK - and she argues that a points-based system does not provide that.

"I want a system where the government is able to decide who comes in to the country. I think that's what the British people want. A points-based system means people just come in automatically, if they meet the criteria."

Theresa May reiterates that Brexit means Brexit - saying the government will deliver on the referendum vote to leave the EU. She says she's been encouraged in bilateral talks with world leaders by "a willingness to talk about opening up trading relationships".

Referring to Japan she said the two countries had been clear they would work together to "maintain and build on our relationship", she adds.

Time for journalists' questions. Asked about whether she's worried that by leaving the single market to satisfy immigration concerns the government could harm the UK economy, Mrs May says she'll be working for the "best deal" for the UK post-Brexit.

She says the referendum result showed the public wanted some control on immigration but she also intends to be "ambitious" in securing a good deal in trade in goods and services.  

"This has been a successful summit. It's demonstrated the important and leading role the UK continues to play in the world," says Theresa May.

She thanks the Chinese government for hosting the "magnificent" summit, and adds that she looks forward to talks with Chinese president Xi Jinping later. She says it'll be an opportunity to discuss how to take forward "the golden era of relations between the two countries" and build a "strong economic and global partnership" that works for both.

Prime Minister Theresa May is holding a news conference following talks at the G20 summit of world leaders in Hangzhou.    

She says leaders have agreed at the summit to "oppose a retreat to protectionism" and committed to ratify the WTO agreement to reduce costs and burdens of moving goods across borders.

On post-Brexit Britain, the PM says she set out the UK's ambition to become "the global leader" in free trade and signalled the country's determination to secure trade deals with countries around the world.

She says India, Mexico, South Korea and Singapore have said they would welcome talks on removing barriers to trade, while the Australian trade minister would visit the UK next week for "exploratory talks".

Mrs May says she'll be chairing a cabinet committee next week to consider trade strategy.

BBC Radio 5 Live

In a ComRes poll commissioned by BBC Radio 5 live, six in ten UK adults (62%) surveyed said they were positive about Britain’s future, after the referendum in June saw the country vote to leave the EU.  

The Daily Politics

Theresa Villiers, former Northern Ireland secretary, is on the Daily Politics programme, and is asked if she's worried Theresa May is going soft on immigration, after the PM ruled out a points-based immigration system advocated by Brexit campaigners during the referendum.

"I really don't believe that she's going soft on immigration," the Brexit campaigner says, adding that reducing immigration is "absolutely central" to what Mrs May wants to do.

Former Labour shadow business minister Chuka Umunna says Brexit campaigners - including Ms Villiers - made a series of pledges during the campaign, including on NHS funding and an Australian points-based system - and that these have been broken.

He says freedom of movement "as we know it" is not sustainable, but he says a points-based system is not the solution.

The Prime Minister's spokesman repeated the line that a points-based system for all migrants to Britain was not an option. He said it was important to design a system that worked for Britain rather than adopt an "off the shelf" model. Discussions are on-going, the daily briefing of political journalists was told.

"Brexit allows us to introduce a system that gives us control over immigration from the EU," he said.

The Prime Minister’s spokesman has said it is up to Keith Vaz to decide whether staying as chair of the Home Affairs Select Committee was tenable.

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