The Conservatives will be supported in parliament by the right-wing Democratic Unionist Party on the basis of an agreement known as "confidence and supply", stopping short of the full coalition government that had been rumoured.
Theresa May said on Friday morning that she would seek to form a government with the assistance of the DUP, hours after losing her party's majority in the general election.
Government Chief Whip Gavin Williamson has been in Belfast on Saturday to open discussions with the DUP on "how best they can provide support" for the Tories, according to a Number 10 source.
That source also said the talks would include the possibility of coalition government, an option which is now understood to be off the table.
An online petition against any Conservative deal with the controversial DUP has already reached 500,000 signatures, and protests have taken place in central London against the alliance.
Under confidence and supply the DUP would not have any of its MPs become government or cabinet ministers, but would support Conservative legislation on a case by case basis. It potentially hands the party more leverage over the Conservatives than a coalition in which they were become part of the government. It will effectively give the Northern Irish politicians the freedom almost to pick and choose between various pieces of legislation they will support. On Brexit, there will be many.
A coalition would have been far more controversial, given the party's stance on issues such as same sex marriage and abortion, but it would have offered greater stability, and may have been the Prime Minister's preferred option.
The party, which is deeply informed by Protestant religious views, has prevented the legalisation of same-sex marriage in Northern Ireland.
A coalition deal would have threatened to undermine the Good Friday agreement, the centrepiece of the Northern Ireland peace process.
Under the terms of the agreement, Unionists and Republicans are supposed to share power, with the Westminster government acting as a broker, and can step in if relations between the two groups, Sinn Fein and the Democratic Unionist Party, break down.
If the DUP were themselves part of the government, the neutral role of the UK government would be compromised.
Sinn Fein leader Gerry Adams has expressed grave doubts over the anticipated deal between the Conservatives and the DUP, in whatever form it takes.
"History will show, alliances between Ulster unionism and British unionism has always ended in tears," he said.
"It is far better to look to our own place, to all of the people here, to deal with the people of this island, this part of the island as one community."
The DUP said that no formal discussions would take place over the weekend. Leader Arlene Foster has said she will come to London on Monday to begin talks with Theresa May.
The Prime Minister has been forced into negotiations after calling a snap election with the expectation of increasing the slender parliamentary majority she inherited from David Cameron, but instead lost it altogether.
Having been twenty points ahead in the polls at the start of the campaign seven weeks ago, the Conservatives won just 318 seats, eight short of an overall majority, and dozens below even modest expectations.
Any formal deal with the DUP will attract harsh criticism. The leader of the Scottish Conservatives, Ruth Davidson, said she had been "given assurances" by the Prime Minister that no concessions would be made over LGBTI rights, an issue Ms Davidson, who is gay and engaged to be married to an Irish Catholic, said was "more important" to her than her party.
Government sources indicate it will cede to demands to the DUP over issues concerning the border with Ireland, and will seek to guarantee on a frictionless border between Ireland and Northern Ireland, and no further checks on travel between Northern Ireland and the UK. But these are thing that all parties involved in the Brexit negotations, including the UK and Brussels, agree on.
The DUP will not seek to impose its hardline agenda on sex marriage and abortion. These matters are already devolved to the Northern Irish Assembly at Stormont.
Tory MP Sarah Wollaston insisted any deal with the DUP must not influence social policy.
The MP for Totnes and former Health minister said: "I will always oppose the death penalty & would resign if others imposed it. They won't.
"I will always support the right for women to choose & access safe termination of pregnancy & will oppose any change to the legislation.
"I will never agree to any dilution of LGBT rights.
"Creationism in schools? Hell no.
"If any of that is a condition of confidence and supply it simply won't work."
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