BELFAST, NORTHERN IRELAND - JUNE 12: DUP leader Arlene Foster holds a press conference at Stormont Castle as the Stormont assembly power sharing negotiations reconvene following the general election on June 12, 2017 in Belfast, Northern Ireland. Discussions between the DUP and the Conservative party are also continuing in the wake of the UK general election as Prime Minister Theresa May looks to form a government with the help of the Democratic Unionist parties ten Westminster seats. Stormont and the political situation in Northern Ireland has been in limbo following the collapse of the power sharing executive due to the Renewable Heat Incentive scheme scandal which implicated the DUP. (Photo by Charles McQuillan/Getty Images)

Britain's Northern Ireland Secretary James Brokenshire arrives for a Cabinet meeting at 10 Downing Street in central London on June 13, 2017. British Prime Minister Theresa May on Tuesday was heading into difficult talks with a hardline Northern Irish party on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

LONDON, ENGLAND - JUNE 13: Secretary of State for Northern Ireland James Brokenshire arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for Foreign and Commonwealth Affairs Boris Johnson arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

LONDON, ENGLAND - JUNE 13: Lord Chancellor and Secretary of State for Justice David Lidington arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

Britain's Home Secretary Amber Rudd arrives for a Cabinet meeting at 10 Downing Street in central London on June 13, 2017. British Prime Minister Theresa May on Tuesday was heading into difficult talks with a hardline Northern Irish party on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

LONDON, ENGLAND - JUNE 13: Secretary of State for Wales Alun Cairns arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for International Development Priti Patel arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

Britain's Environment, Food and Rural Affairs Secretary Michael Gove arrives for a Cabinet meeting at 10 Downing Street in central London on June 13, 2017. British Prime Minister Theresa May on Tuesday was heading into difficult talks with a hardline Northern Irish party on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

LONDON, ENGLAND - JUNE 13: Secretary of State for Foreign and Commonwealth Affairs Boris Johnson arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Leon Neal/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for Communities and Local Government Sajid Javid arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

LONDON, ENGLAND - JUNE 13: Attorney General Jeremy Wright QC arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Jack Taylor/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for Transport Chris Grayling arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Leon Neal/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for Work and Pensions David Gauke arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Leon Neal/Getty Images)

International Trade Secretary Liam Fox arrives at 10 Downing Street in London for a Cabinet meeting. PRESS ASSOCIATION Photo. Picture date: Tuesday June 13, 2017. See PA story POLITICS Election. Photo credit should read: Dominic Lipinski/PA Wire

LONDON, ENGLAND - JUNE 13: Secretary of State for Exiting the European Union David Davis arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Leon Neal/Getty Images)

LONDON, ENGLAND - JUNE 13: Secretary of State for Business, Energy and Industrial Strategy Greg Clark arrives at Downing Street on June 13, 2017 in London, England. The Prime Minister has re-shuffled her cabinet after the snap general election which failed to return a clear overall majority winner. Theresa May is set to meet Northern Ireland's Democratic Unionist Party leader Arlene Foster later today in hope of making an agreement to form a minority Government. (Photo by Leon Neal/Getty Images)

DUP leader Arlene Foster and DUP deputy leader Nigel Dodds arriving at 10 Downing Street in London for talks on a deal to prop up a Tory minority administration. Dominic Lipinski/PA Wire

Democratic Unionist Party (DUP) leader Arlene Foster (L), and DUP Deputy Leader Nigel Dodds arrive at 10 Downing Street in central London on June 13, 2017, for a meeting with Britain's Prime Minister and Conservative Party leader Theresa May. British Prime Minister Theresa May on Tuesday was heading into difficult talks with the DUP on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

LONDON, ENGLAND - JUNE 13: DUP leader Arlene Foster checks her watch as she arrives at 10 Downing Street on June 13, 2017 in London, England. Discussions between the DUP and the Conservative party are continuing in the wake of the UK general election as Prime Minister Theresa May looks to form a government with the help of the Democratic Unionist party's ten Westminster seats. (Photo by Leon Neal/Getty Images)

Democratic Unionist Party (DUP) leader Arlene Foster (R), and DUP Deputy Leader Nigel Dodds arrive at 10 Downing Street in central London on June 13, 2017, for a meeting with Britain's Prime Minister and Conservative Party leader Theresa May. British Prime Minister Theresa May on Tuesday was heading into difficult talks with the DUP on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

DUP leader Arlene Foster and DUP deputy leader Nigel Dodds arriving at 10 Downing Street in London for talks on a deal to prop up a Tory minority administration. Dominic Lipinski/PA Wire

Democratic Unionist Party (DUP) leader Arlene Foster (L), and DUP Deputy Leader Nigel Dodds arrive at 10 Downing Street in central London on June 13, 2017, for a meeting with Britain's Prime Minister and Conservative Party leader Theresa May. British Prime Minister Theresa May on Tuesday was heading into difficult talks with the DUP on securing a working majority after a crushing electoral setback. / AFP PHOTO / Ben STANSALLBEN STANSALL/AFP/Getty Images

DUP leader Arlene Foster and DUP deputy leader Nigel Dodds arriving at 10 Downing Street in London for talks on a deal to prop up a Tory minority administration.Dominic Lipinski/PA Wire

LONDON, ENGLAND - JUNE 13: DUP leader Arlene Foster checks her watch as she and MP Nigel Dodds arrive at 10 Downing Street on June 13, 2017 in London, England. Discussions between the DUP and the Conservative party are continuing in the wake of the UK general election as Prime Minister Theresa May looks to form a government with the help of the Democratic Unionist party's ten Westminster seats. (Photo by Leon Neal/Getty Images)

DUP leader Arlene Foster and MP Nigel Dodds arrive at 10 Downing Street on June 13, 2017 in London, England. (Photo by Jack Taylor/Getty Images)

DUP leader Arlene Foster has held her Downing Street meeting with Prime Minister Theresa May on a deal which could prop up a Tory minority government, with sources saying there has been "significant progress" made.

The DUP leader entered Downing Street just after 12.30pm on Tuesday. She smiled at the waiting media as she and the DUP's leader at Westminster Nigel Dodds entered Number 10.

At a photocall ahead of the meeting with her 10 members of parliament, Arlene Foster said: "The future's bright" to which MP Ian Paisley added: "The future's orange".

Shortly after 2pm Theresa May left Downing Street in a waiting car.

Sky News reported that the DUP delegation left via a side door. Talks are set to continue after the election of a speaker in the House of Commons on Tuesday afternoon.

In a tweet, Mrs Foster said discussions were going well and she hoped to bring the work to a successful conclusion.

Downing street described the talks as "constructive".

Later speaking in the Commons on the election of the Speaker John Bercow, Nigel Dodds said he "looked forward" to this Parliament. He said, given the SDLP and UUP absence, he and the other Northern Ireland MPs bore a "huge responsibility" and they will carry out their responsibilities "very carefully".

He said he looked forward to devolution being restored in Northern Ireland "so all can take part in governing Northern Ireland".

"We have interesting times ahead and I look forward to playing a full role in this Parliament," he said.

In his opening remarks Jeremy Corbyn said: "I'm sure we all look forward to welcoming the Queen's Speech, just as soon as the coalition of chaos has been negotiated."

Discussions are going well with the government and we hope soon to be able to bring this work to a successful conclusion. — Arlene Foster #WeâllMeetAgain (@DUPleader) June 13, 2017

The Prime Minister will be desperate to get agreement from the DUP to back her legislative programme in the House of Commons or risk her government falling.

Mrs May’s authority has been severely diminished after a disastrous general election which saw her lose her Commons majority and a deal with the DUP looks vital for the continuation of Tory rule. There has been much speculation on what could be on the DUP wish list as part of the negotiations.

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A failure to gain support from the Northern Irish party would risk the Queen’s Speech being voted down next week, and Jeremy Corbyn has said Labour will be pushing hard for that outcome.

The Tories and the DUP are considering a “confidence and supply” arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.

It comes after Mrs May told Tory MPs: “I’m the person who got us into this mess and I’m the one who will get us out of it.”

Her most senior minister Damian Green has confirmed the Queen’s Speech setting out the Government’s programme could be delayed if a deal is not reached in time for it to go ahead on Monday as planned.

Belfast Telegraph