The results, if confirmed, would mark a stunning setback for May, who had called the vote to strengthen her hand before Brexit talks but could emerge grievously weakened.
The exit poll showed May's Conservative Party winning 314 seats in Britain's 650-member Parliament, leaving it short of the total needed for a majority and 17 behind the number it won in 2015. The Labour Party was projected to win 266 seats in Parliament, up 34 seats from the results two years ago.
The results raise questions about whether either major party will have enough support to form a government without resorting to forming a coalition - a scenario known as a hung parliament.
If it comes to that, it's far from clear which parties would team up, or under what arrangements. A "progressive coalition" - including Labour, the Liberal Democrats, Scottish and Welsh nationalists, and others - may have as many seats as the Tories. But the Conservatives would also have potential coalition partners if they fall short of a majority, including unionists in Northern Ireland.
In the early minutes after the exit polls' release, the pound fell 2 percent as investors reacted to potential political turmoil. Sterling dropped to 1.2750 against the U.S. dollar, its lowest levels since May's call for a snap election in April.
Conservatives were incredulous as the exit poll numbers emerged, saying they thought the results had undersold the party's performance and that official tallies would give them a higher total.
"Let's see some actual results to see if this is borne out," British Defense Secretary Michael Fallon told the BBC. He noted that the exit polls in 2015 initially pointed to a hung parliament but that Tories ultimately won a majority.
Guardedly optimistic Labour leaders, meanwhile, were talking about the possibility of May having to step down.
"If it is right, I think her position is becoming increasingly untenable," John McDonnell, Labour's shadow chancellor, told the BBC about May's premiership.
In Europe, observers were bracing for more instability out of Britain.
"Could be messy for the United Kingdom in the years ahead," tweeted former Swedish prime minister Carl Bildt. "One mess risks following another. Price to be paid for lack of true leadership."
May had acknowledged that a result such as the one signaled in the exit polls would be a defeat.
"If I lose just six seats I will lose this election, and Jeremy Corbyn will be sitting down to negotiate with the presidents, prime ministers and chancellors of Europe," she wrote on her Facebook page last month.
Although exit polls have been imprecise in past elections, they are seen as a fairly reliable guide to the overall results. Official tallies will stream in through the night in Britain, with the final outcome not known until early Friday local time or about midnight EDT.
The exit poll results, if accurate, will draw renewed scrutiny to May's choice to gamble by going back on repeated promises not to call an election before the one that had been due in 2020. They could also leave Britain rudderless just as what are sure to be contentious talks are scheduled to get underway with European leaders over the terms of Brexit.
May in April broke her vows not to call a snap vote, telling the country that she needed a stronger mandate before she begins Brexit talks.
Corbyn spent little time during the campaign discussing Brexit. Like May, he favored "remain" during the referendum. But also like May, he has promised not to obstruct the will of voters and to follow through on their desires for an exit if he is elected.
The election follows a turbulent campaign that was interrupted by two mass-casualty terrorist attacks, and that had been marked by a faltering performance by May even as Corbyn exceeded expectations.
Despite security concerns, the election unfolded peacefully from the remote Scottish isles to the bustling lanes of London, with Britons using stubby pencils to mark their ballots at schools, church halls, pubs, railway cars and other voting sites nationwide.
When May called the vote, observers hailed the move as a cunning bit of political strategy and predicted she would win in a landslide that could deliver her the sort of overwhelming parliamentary majority that predecessors Margaret Thatcher and Tony Blair had enjoyed.
May came to power last year, emerging to claim the nation's top job following the political wreckage of the country's astonishing choice to leave the European Union.
Since then she has had only a slender majority in Parliament - won in a 2015 election when the country was governed by her predecessor, David Cameron - and she had feared that without a bigger cushion she would lack the latitude she needs for Brexit talks.
Early pre-election polls suggested she would get what she wanted, with the Tories enjoying leads of 20 points or more over the far-left Corbyn and his Labour Party.
In the final days of campaigning, polls showed the Tory lead withering to as little as a single point.
"We've learned what we suspected all along: She's not particularly fast on her feet, she's not a natural campaigner, she's not really a people person," said Tim Bale, a politics professor at Queen Mary University of London.
Lacking the common touch, May's strategy was to focus the campaign on a presidential-style choice between her leadership skills and those of Corbyn. She relentlessly hammered her rival as a far-left throwback to another era who would leave the country vulnerable in both the Brexit talks and at a time of growing terrorist threats.
Corbyn - for decades a far-left backbencher who unexpectedly vaulted to the party's leadership in 2015 - faced a steeply uphill challenge to sell himself as a potential prime minister.
But he was widely seen to have mounted a far more credible challenge than many thought possible, running a nothing-to-lose campaign focused on ending seven years of Tory austerity and shrinking the gap between rich and poor.
Even if he doesn't prevail, his performance may have helped his chances of hanging on as Labour leader - a stinging blow for more-centrist party figures who had quietly hoped the harsh glare of a national campaign would leave him exposed and force him to step aside.
Corbyn has run a "fantastic campaign," said Henry Wynn, 72, a retired professor who described the Labour leader as a "Bernie Sanders socialist" after he voted for Corbyn's party in the north London neighborhood of Islington.
But Wynn seemed to hold out little prospect for victory.
"I'll confess," he added, "we're in a mildly depressive mood. We face a bleak future with the Tories."
May helped her cause by consolidating support not only among those who had favored Brexit in last year's referendum, but also voters who, like May, had backed the "Remain" cause but have pivoted since the vote to accepting the outcome and focusing on how to get the best deal out of Europe.
Miranda John, a 52-year-old mortgage broker who lives in south London and was one of the first to vote after polls opened at 7 a.m., said she voted for May's Conservative Party "because of fears of Brexit" and her belief that the Tories have "a better negotiation team."
"I was a Remainer," she said, referring to the EU referendum held last June. "But I accept that the will is to leave, so we need to get the right deal."
Negotiations with the remaining 27 members of the EU are due to kick off in a little over a week. Assuming May is still leading Britain by then, she faces long odds in delivering the successful exit that she has promised.
May has vowed a hard break with the bloc that leaves Britain outside the single market, the customs union and the European Court of Justice. But she has also promised to deliver a free-trade deal that will preserve the best elements of membership without many of the onerous burdens.
European leaders scoff at such notions, and say Britain's demands for EU benefits without responsibilities will have to be denied lest the country's departure trigger a rush to the exits by other nations that all demand the same sweetheart deal.
If she prevails, May will also be under pressure to deliver on pledges to expand the powers of police and other security services following the mass-casualty terrorist attacks this spring, including two in the midst of the campaign.
On May 22, a suicide bomber killed 22 people - including numerous teenage girls - at the conclusion of a concert by American pop star Ariana Grande in Manchester. In London, eight people died following a van-and-knife rampage around the bustling London Bridge area last Saturday.
After that latest attack, May said "enough is enough" and promised a sweeping review of the nation's counterterrorism rules, with an eye to giving authorities more power to lock up the kind of peripheral figures in extremist circles who have been responsible for the recent attacks.
After the attacks, many observers thought they would play to May's advantage. But Corbyn managed to flip an area of weakness - security - to a potential strength by hitting out at May for the cuts to police budgets she had authorized as the nation's home secretary, the top domestic security official.
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