Image source, PA

The Irish Prime Minister said he and Theresa May had committed to working together to urge the parties in Northern Ireland to come together before the deadline of June 29 to form a new executive.

Northern Ireland has been without a power-sharing executive since March and without a first and deputy first minister since January after a bitter row between the DUP and Sinn Féin about a botched green energy scheme.

Leo Varadkar said the people of Northern Ireland had voted for devolution and should have a unique voice at this time.

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BBC News Channel

Ireland's new prime minister Leo Varadkar says it is "a matter of regret" the UK is leaving the EU, the single market and the customs union.

"We would prefer it was not so, but this is the sovereign decision of the people of the United Kingdom," he said, following talks in Downing Street with Theresa May.

He said the two sides had agreed there should not be a hard border between Northern Ireland and the Republic, so trade can continue as it did before.

BBC News Channel

Irish Prime Minister Leo Varadkar says he is "very reassured" that there will be no conflict of interest from the deal being struck between the Conservatives and DUP.

Mr Varadkar said he did relay his "concerns" about the DUP getting too close to the UK governing party during talks at Downing Street.

But he said he was reassured by Theresa May's pledge to make public the final agreement between the two parties.

Mr Varadkar said it was important the UK and Ireland remained "impartial actors" when it comes to Northern Ireland, especially as both governments are co-guarantors to the Good Friday agreement.

Mrs May said she remained "absolutely committed" to working with all the Northern Ireland political parties and had met all five of them last week.

Leo Varadkar told the news conference his country was "saddened" that the UK had voted to leave the EU, but respected the wish of the British people.

He and Theresa May had "spoken in detail about Brexit", he said, mentioning his desire to maintain the "reciprocity of civic rights between the UK and Ireland" - the rights of citizens of each country to be treated the same.

This right had been present "since independence" and even earlier, the Taoiseach said, adding that there should be "minimal disruption" to trade between the two countries over Brexit.

The World at One
BBC Radio 4

A minister in the Department for Exiting the European Union has said "any objective observer" will be "deeply reassured by what we're putting on the table" for Brexit proposals.

Steve Baker, who was recently appointed to the department by Theresa May, told Martha Kearney he is "confident we will make swift progress" and that the work of the department is "very high quality".

Mr Baker said that securing the rights of EU citizens in the UK and UK nationals in the EU was "our first priority" in the negotiations. On the issue of the divorce bill he said they would arrive at a position where the UK "pays what it owes in a proper manner consistent with our reputation for obeying the rule of law".

BBC News Channel

Image source, EPA

It's more important than ever that the relationship between Ireland and the UK goes from "strength to strength" in the wake of Britain leaving Europe, Theresa May has said.

Following talks with the Irish Prime Minister Leo Varadkar, the UK PM said: "We're leaving the EU but we're not leaving Euorpe and we want to remain committed partners and allies of Ireland and all our friends across the continent."

Mrs May hailed the trading relationship between the two countries, which is worth over £43bn a year and supports 400,000 jobs, adding that "no-one wants to see this diminished".

She said the UK was committed to finding a practical solution for the land border in between Northern Ireland and the Republic after Brexit.

She also wants reciprocal rights for citizens "guaranteed" and resolved "as a matter of priority".

Leo Varadkar spoke at the news conference of the close bonds between the UK and the Irish Republic, saying he wanted to "enhance those close bonds of friendship".

He offered his country's sympathy for the "enormous tragedies" the UK had faced in recent days, weeks and months, saying that the links between the people of the two countries made it seem as if the attacks had occurred at home.

Quoting Churchill, he said our two countries "should walk together in mutual comprehension and forgiveness", united in shared ambitions to find solutions.

There is "a crucial need" for Northern Ireland's political parties to reach an agreement to form a "fully functioning" executive by 29 June, Theresa May has said, following talks with the new prime minister of Ireland, Leo Varadkar.

Speaking in Downing Street, Mrs May said the UK and Ireland "will do everything we can to work with them".

She said it is her firm belief "that with goodwill on both sides", a resolution can be reached that builds on the progress made.

The UK government is "absolutely committed" to a successful outcome and remains steadfast in its support for the Belfast agreement, Mrs May added.

Image source, PA

The new Taoiseach - Prime Minister of the Irish Republic- is in Downing Street for talks with Theresa May.

Leo Varadkar has said he wants to renew the close bond and strong relations that exist between Ireland and the UK.

Brexit and the breakdown of devolution in Northern Ireland are on the agenda.

Read more.

Ian Duncan believes the devolved nations should have a voice as Brexit details are being hammered out.

The Daily Telegraph

Image source, Reuters

According to the Daily Telegraph, external, while many meetings in Brussels are accompanied with fine wine, it appears the Brexit negotiations , externalmay be a very dry affair.

Eurocrats have been advised to stay sober during the talks because of the heatwave, the paper reports.

It also appears David Davis will be conducting talks with Michel Barnier, the EU chief negotiator, external in the dark, as staff have been told to switch off all the lights., external

His talks may also finish early, as EU staff have been told they can leave work at 4pm if the weather is too warm, the paper adds.

Read more, external

Image source, Reuters

The BBC has been told by European Union sources that the talks will follow the EU's preferred pattern of exit negotiations first, with the future relations between the two sides - including the free trade deal the UK is seeking - at a later date.

On this, the first day of formal negotiations, the EU's chief negotiator Michel Barnier said a "constructive" opening to negotiations was vital in setting the tone for what he hoped would be an "orderly" process.

"We must first tackle the uncertainties caused by Brexit - first, for citizens but also for the beneficiaries of EU policies and for the impact on borders, in particular Ireland," he said.

Alex Forsyth
Political correspondent

Image source, Reuters

Brexit Secretary David Davis and the EU's chief negotiator Michel Barnier exchanged gifts that reflected their "shared love of climbing and mountaineering" as the first formal Brexit talks got underway in Brussels.

From Mr Davis there was a first edition of a mountaineering book - a French language version of Regards vers Annapurna - signed by Marcel Ichac, one of the two authors.

From Mr Barnier, a traditional walking stick from Savoie which is made from wood, hand carved and has a leather wrist strap.

For lunch the two key negotiators had Belgian asparagus, red mullet with vegetables and fondant potatoes, meringue cake with wild strawberries and mocha coffee and cakes to round it off.

BBC News Channel

Labour's shadow Brexit secretary Sir Keir Starmer says his party hopes his opposite number, David Davis, will achieve "a good deal for the country".

But he accuses the prime minister of starting the Brexit negotiations "in the worst of all situations", claiming her "mandate is unclear" and she "has lost authority abroad".

Sir Keir says this is in contrast to Labour's "consistent" position of wanting the UK to retain the benefits of the customs union and single market for British jobs.

He adds that Theresa May has been "far too quick to take options off the table".

What does Brexit mean?

It is a word that has become used as a shorthand way of saying the UK leaving the EU - merging the words Britain and exit to get Brexit, in a same way as a possible Greek exit from the euro was dubbed Grexit in the past.

Why is Britain leaving the European Union?

A referendum - a vote in which everyone (or nearly everyone) of voting age can take part - was held on Thursday 23 June, 2016, to decide whether the UK should leave or remain in the European Union. Leave won by 51.9% to 48.1%. The referendum turnout was 71.8%, with more than 30 million people voting.

Read a full guide to Brexit

Identity cards are "plain common sense" says former Labour Home Secretary Charles Clarke.

Image source, Getty Images

What are the options for those beginning the negotiations for Britain's departure from the European Union?

Do you know your 'hard' Brexit from your 'soft' Brexit?

Find out here.