LONDON—David Cameron was on track to win an astonishing victory in the British election on Thursday night.

Early results and exit polls suggested the Conservative leader would fail to secure a majority in the House of Commons, but he would be in a strong position to form a government that would be expected to rule Britain for the next five years.

The electorate was given an unusually stark choice: Cameron, the incumbent, pro-business product of Britain’s poshest school, or Ed Miliband, the geeky son of a Marxist intellectual, who would become Britain’s most left-wing leader in a generation.

The scale of the Conservatives’ unforeseen victory will be studied by political advisers and historians all over the world as the opinion polls utterly failed to capture the way the votes would be cast.

The swing to Labour that was consistently predicted in months of intensive polling dramatically failed to appear on a night of shocks in all parts of the country. Labour was wiped out by the buoyant Scottish National Party in the North. “There’s a lion roaring in Scotland tonight. A Scottish lion,” said former leader Alex Salmond.

The most remarkable SNP winner was little more than a cub. Mhairi Black, a 20-year-old politics student, comfortably defeated the man who ran Labour’s election campaign, Douglas Alexander. She becomes the youngest member of Parliament since 1667.

If the results continue in the same vein, Cameron will be under pressure from the right of his party to go it alone as a minority government with no coalition partners. That means he would be unable to guarantee the passage of any laws but would not need to negotiate away any of the party’s policies in secretive meetings with rival parties.

There has not, however, been a stable minority government of Britain since the 1930s.

If the Liberal Democrats lose more than three-quarters of their seats, as the exit polls suggest, the Conservatives would no longer be able to turn to their old colleague Nick Clegg, the deputy prime minister, to help them form a stable majority government.

The opinion polls for the last year indicated that Cameron had a daunting task. He was always expected to secure the most MPs but faced the massed ranks of at least seven anti-Tory parties who were expected to gang up and deny him the ability to govern.

Ed Miliband, the Labour leader, fought a unexpectedly well-received campaign, but he has fallen at the final hurdle. Britain’s newspapers, which waged an unprecedented war of hostility against Miliband, will be declaring victory Friday morning.

Peter Kellner, president of leading pollster YouGov, told The Daily Beast that Labour was unlikely to threaten Cameron’s ability to govern even if there is no stable majority government. “The worst thing for an opposition party to do in the immediate aftermath of an election is act in a way which makes Britain ungovernable,” he said.

The Lib Dems had been expected to be kingmakers once again, but they have suffered a rout. Many people wanted to see them punished for accepting the trappings of office and propping up the Conservatives in the last coalition in exchange for giving away some of their most well-known policy principles.

The exit polls suggested the collapse of the Lib Dems would be the most decisive shock of the night. Their hemorrhaging of support allowed the Conservatives to arrest their expected slide.

The first signs of trouble emerged earlier in the day, when Liberal Democrats—who had a strong lead to defend in the seat of Hornsey and Wood Green in North—began to accept that they were on course for defeat.

The suburban district was only 93rd on Labour’s target list, but the Liberal Democrats could not resist a national mood of recriminations against them, after they were seen to have sold out after the 2010 election. “Most of Europe is ruled by coalitions, but people here just can’t get their heads around what we did,” a party official told The Daily Beast.

Labour activists expressed their delight, but the exit polls suggested that this potential Labour bright spot was simply a side effect of a nationwide Liberal Democrat collapse. Professor Patrick Dunleavy, from the London School of Economics’ Department of Government, said the party’s decision to join Cameron’s coalition proved fatal. “This is existentially disastrous for them,” he said. “Their very existence as a party is in jeopardy.”

Victory for Cameron will ensure that he keeps rivals Boris Johnson and Theresa May at bay for a while, but his expected failure to win an outright majority for the second election running still leaves him vulnerable. “The paradox is that David Cameron survives as PM but as a minority government that has no power to do anything,” Dunleavy said. “By comparison with every other conservative leader in the last 100 years, he is a feeble no-hoper.”

If Cameron does lead a minority government, one of his first orders of business will be the European referendum he promised. As part of his pitch to persuade U.K. Independence voters to return home to the Conservatives, he pledged to hold an in/out referendum on membership in the European Union. His party is dangerously split on the issue that will now dominate the next two years of British politics.

That will only serve to highlight the scale of his task in keeping a minority government together. The last time it happened, in 1978 and ’79, Jim Callaghan’s Labour government ended up limping from vote to vote, with people on stretchers and oxygen tanks forced to take part in crucial votes.

Tony Travers, a former civil servant and political adviser, told The Daily Beast: “Since the war, the only periods of minority government have ended messy and with the government not in control of their own destiny.”