Or, either the Conservatives or Labour could attempt to govern as a minority administration, seeking to win support in the Commons for their programme on a vote-by-vote basis.
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".
Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd, Defence Secretary Michael Fallon and Brexit Secretary David Davis have all been kept on in their roles.
The forecast is slightly better for the Tories than the exit poll published when polls closed on Thursday night but would still potentially leave May with fewer MPs than when she called the general election to "strengthen her hand" in the upcoming Brexit negotiations.
"I'm never going to give in arguing for what I believe is a pathway to a majority Labour government", he added.
Results so far suggest that May's party could struggle to retain its overall majority in Parliament.
The Green Party, SNP, Plaid Cymru have all spoken in favour of alliances, although the Liberal Democrats - for whom a coalition with the Conservatives has already proved devastating - had ruled out joining with other parties. She vowed to take the country out of the EU's single market and customs union, essentially a free-trade zone, radically changing Britain's relationship with one of its biggest trading partners.
"It is the policy of both the Conservative party and the UK Labour party to respect the Brexit referendum result".
George Osborne, the former finance minister who stepped down at the election, told ITV that the results were "catastrophic" for his party.
Official Brexit negotiations are set to start in 11 days. DUP leader Arlene Foster confirmed plans to hold talks with the Conservatives to discuss a way "to bring stability to our nation at this time of great challenge". She said it would help her in negotiating Britain's exit from the European Union.
The Tories, as they are commonly known in the United Kingdom, will now have to govern as a minority party, or try to form a coalition government, or force another general election.
Former Conservative minister Anna Soubry added that the premier "is in a very hard place. she now has to obviously consider her position".
Her opponents also took issue with her refusal to take part in a televised debate with other party leaders.
The Scottish National Party of First Minister Nicola Sturgeon, which has dominated politics north of the border for a decade, and called for a new independence vote after Brexit, lost 21 of the 56 seats it won in 2015.
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