Australia names first indigenous ministerpublished at 08:59 Greenwich Mean Time 18 January 2017
The rise of conservative politician Ken Wyatt, the first indigenous Australian to become a minister.
Read MoreMay speaks about Brexit at Davos
Says UK to lead world on free trade
Audience is mainly business leaders
IMF's Lagarde warns UK of Brexit pain
UK to trigger EU exit talks by April
Alex Hunt, Jackie Storer and Emma Griffiths
The rise of conservative politician Ken Wyatt, the first indigenous Australian to become a minister.
Read MoreBBC Breakfast
Shadow Brexit Secretary Keir Starmer says he is concerned that a disorderly exit could leave the UK with "no meaningful relationship" with the EU.
‘What I was highly critical of yesterday was Theresa May's sort of bargain basement tax haven threat," he told BBC's Breakfast
"That would make people poorer, there's no mandate for it and it is totally inconsistent."
Jeremy Corbyn, who will face Theresa May later at Prime Minister's Questions, echoed this view by tweeting that he would fight any attempt to turn the UK into a "tax haven on the edge of Europe".
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Today Programme
BBC Radio 4
Asked if he guarantees there won't be any customs checks in future, Brexit Secretary David Davis says he can't, but his aim is for a customs agreement that is as "frictionless as possible" - repeating a phrase that Mrs May used yesterday.
He rejects suggestions that the Civil Service simply isn't equipped to deliver Brexit, saying he has spoken to senior mandarins in every single department and they all think it is possible.
He quotes former cabinet secretary Robin Butler as saying that if the civil service can cope with World War Two, it can cope with this.
In conclusion, he says he hopes Brits will see their economic prospects enhanced by Brexit while the UK remains "good friends" with its neighbours.
Today Programme
BBC Radio 4
Parliament will have debates and votes through the Brexit process, not just on the final deal, Brexit Secretary David Davis says. He cites other looming legislation such as the Great Repeal Bill.
Asked what happens if MPs block the settlement, Mr Davis suggests that this "will not reverse" Brexit as the government has already been given a mandate to proceed by the referendum decision.
Quote MessageParliament will not vote it down. This negotiation will succeed."
Today Programme
BBC Radio 4
David Davis echoes Boris Johnson by saying there are a huge number of countries that are keen to do free trade deals with the UK - he names Canada, New Zealand, Australia and the US among them.
He says his goal is the best possible deal - both for the UK and the EU.
He is pressed by John Humphrys on how long the process may take. Mr Davis says he believes the fundamental negotiations can be done in two years although he agrees that the implementation phase may take longer.
Asked how long - John Humphrys mentions five years - Mr Davis says it won't take that long and says the public wants the government to get on with it.
Quote MessageWe need to do this expeditiously and that is what we are going to do."
Today Programme
BBC Radio 4
Brexit Secretary David Davis tells the BBC that Mrs May's speech was "overwhelmingly positive" - describing it as one of the best speeches he has heard from a prime minister for a "long time".
Quoting Donald Tusk - who said Mrs May's ideas were "realistic" - he says the EU's response has been measured and there hasn't been the "push back" that you would expect at this early stage.
Pressed about criticism of the UK's approach from European Parliament negotiator Guy Verhofstadt, Mr Davis says "Guy is only one player in this".
Mr Davis says the UK wants a constructive relationship with the EU going forward, in areas like trade and security, but he says what the UK will not "take" is any kind of settlement designed to punish the UK.
BBC Economics Correspondent Andrew Walker answers your questions on Theresa May's Brexit speech.
Read MoreToday Programme
BBC Radio 4
Tomas Prouza, the Czech Republic's secretary of state for EU affairs, tells Today that he thinks David Cameron could not have gotten any more from the EU in his negotiations. Mr Prouza says Cameron's attitude to the EU was all wrong, as it suggested "We like your money but we don't like your people". Mr Prouza says that this is not the Europe anyone wants to see.
It was, all in all, an assured performance by the prime minister. She looked and sounded confident as she delivered her Plan for Britain. But it might be thought appropriate to note the ironies and even potential contradictions.
Read MoreExiting the European Customs Union creates a "hard border on the island of Ireland", Sinn Féin says.
Read MoreUnsurprisingly, Wednesday's front pages (see below) are all about Theresa May's Brexit speech. On Wednesday we're expecting to hear what the main players in Brussels made of it. Back at Westminster, it's PMQs at midday.
Here's some reading in the meantime:
Laura Kuenssberg's verdict on the PM's speech
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BBC journalist tweets...
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