Instead, voters stripped the Conservatives of their parliamentary majority.
A Downing Street spokesman said that the Prime Minister will visit Buckingham Palace at 12.30pm on Friday to speak to the sovereign.
Labour Party leader Jeremy Corbyn, speaking after being re-elected in Islington North, said it was time for Mrs May to "make way" for a government that would be "truly representative of the people of this country".
The Conservatives, who remain the largest party with 318 seats, lost their majority on a night full of shocks.
Thank you x 292,316.
Davidson, one of the few Conservatives to emerge as a victor from the election after she increased the party's presence in Scotland, said she had demanded, and received, "categoric assurance" from May that the policy would not change.
"She will need to worry about maintaining the support of Conservative MPs who are both critical of Europe and critical of her decision to hold an election and squander the Conservative party's majority", said John Bartle from the University of Essex.
"May won't be able to make any compromises because she lacks a broad parliamentary majority", he said.
"The success of the Labour Party winning more seats than expected was because they tapped into anxiety over public spending cuts since 2010, anxiety over the state of National Health Service, and also concerns with youth voters over the amount of student debt and access to United Kingdom housing - two big issues".
Many analysts said it was unlikely May could remain leader for long now that her authority has been eroded.
The DUP is "likely to increase the pressure on Theresa May to secure a comprehensive free trade agreement", said Stephen Booth of the Open Europe think tank.
The DUP and Conservatives have been in close touch throughout Mrs May's year in power, and contacts are believed to have continued as election results came in this morning. Northern Irish political party.
Former Tory leader Lord Hague said "very serious lessons" had to be learned by the party but warned against a leadership contest.
The London Evening Standard, edited by former finance minister George Osborne who was sacked by May, splashed with a photo of her under the headline "Queen of Denial".
But her party is deeply divided over what they want from Brexit and the result means British businesses still have no idea what trading rules they can expect in the coming years.
Theresa May has lost her mandate.
As the party with the most seats and votes "it will be incumbent on us to ensure that we have that period of stability and that is exactly what we will do".
At the time she was riding high in the polls and she pushed a tough message on Brexit on the campaign trail, saying she was planning to be a "bloody hard woman" in Brussels.
She insisted that she would stick to the Brexit timetable.
"We have discovered that she is a competent minister, potentially a tough negotiator, but a bad campaigner", he said. "We should have been getting in there".
Britain's typically pro-Conservative press savaged May on Saturday and questioned whether she could remain in power, only two months after she started the clock ticking on the two-year European Union divorce process.
Leader Tim Farron held on to his Westmorland and Lonsdale seat in Cumbria on a much-reduced majority, down from 8,949 in 2015 to just 777 now.