Cable, beaten in the 2015 election, regained a parliamentary seat in Thursday's general election, which ended with the Conservatives being forced to form a minority government.
Prime Minister Bill English today congratulated Theresa May on her re-election as British Prime Minister.
After confirming on Friday that her top five ministers would keep their jobs, including finance minister Philip Hammond, May is expected to continue to appoint the government that will take on one of the most demanding negotiations in British history.
Downing Street said the outline agreement will be put to the Cabinet for discussion on Monday.
Britain's typically right-wing press savaged May over the election outcome, questioning whether she will be able to remain in power after a result that leaves her reliant on uniting rival factions within her party to deliver Brexit.
Neither side is seeking a formal coalition, of the sort Britain saw in 2010. "That's not a matter for me", she said.
The British pound tumbled on Friday against the USA dollar and the euro before stabilising, down 1.7 and 1.4 percent against the two currencies respectively.
Several lawmakers demanded the resignation of May's top advisers, who have been widely blamed for a disastrous policy to make the elderly pay more toward their care and a campaign seen as too insulated from ordinary voters and too focused on attacking her opponent.
May has said Brexit talks will begin on June 19 as scheduled, the same day as the formal reopening of parliament. The party's leader Arlene Foster was elected previous year on a promise to work to prevent abortion rights from being extended to Northern Ireland.
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Since then, Trump administration officials have tried to walk back the damage, and talk Gulf states off the ledge. Tillerson praised efforts by Kuwait to mediate the crisis and said Washington would support the emir of Kuwait.
Britain's typically pro-Conservative press questioned whether Mrs May could remain in power with the clock ticking on the two-year European Union divorce process.
One senior party source said that as long as MPs do not feel isolated and there are enough of them, they will come back.
May had repeatedly ruled out the need for a new election before changing her mind.
But despite jubilation among Mr Corbyn's supporters at bloodying Mrs May' s nose, Labour MP Chris Leslie said the party should not pretend it achieved a "famous victory". "The task of restoring orderly government in order to make sense of Brexit is now a national emergency, and it falls to them".
If May is to succeed in delivering the wish of the 52 percent of voters who opted a year ago to take Britain out of the European Union, she must find a way to bridge the differences within her party to pass laws preparing for and enacting the departure.
Managing that process will not be easy. The eurosceptic wing of the party has always been a thorn in the side of Conservative prime ministers.
DUP leader Arlene Foster, whose party won 10 seats, had said Friday that she was ready to talk to the Conservatives on "how it may be possible to bring stability to our nation".
The DUP is "likely to increase the pressure on Theresa May to secure a comprehensive free trade agreement" in place of its single market membership, said Stephen Booth of the Open Europe think tank.
But Scottish Conservative leader Ruth Davidson, who is gay, was among the first to express disquiet over a deal with the DUP, which is opposed to abortion and gay rights.
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