LONDON—An early exit poll suggests British Prime Minister Boris Johnson is set to win a large majority in Thursday’s general election, an outcome that would mark a stunning victory for the Brexit cheerleader and pave the way for the U.K. Parliament to trigger a long-awaited split with the European Union.

The exit poll commissioned by three national broadcasters, released just after polling stations closed Thursday, said Mr. Johnson’s Conservative Party was on track to win 368 seats in Britain’s 650-seat House of Commons. The main opposition Labour Party was forecast to win 191, with smaller parties taking the rest.

That would suggest Mr. Johnson’s party will have 86 more seats all the other parties combined, which would be the largest majority for any party since Tony Blair’s Labour victory in 2001.

If the opinion poll is borne out by the actual result, the Conservatives would have won more seats than in any election since Margaret Thatcher won for a third time in 1987. It would be the Labour Party’s worst performance in terms of lawmakers elected since 1935.

The poll asks tens of thousands people how they voted and has correctly forecast the outcome of two out of the last three elections. Its organizers say they should be able to predict the seats won by each of the main parties to within 10 or 15 seats.

“Brexit has dominated, we thought other issues could cut through,” said John McDonnell, a Labour spokesman. “But they haven’t.” He said the results, if correct, were “extremely disappointing.”

Mr. Johnson’s expected triumph came on the back of a simple message that a vote for the Conservatives would “Get Brexit Done.” It was supplemented by promises of extra government spending to reverse some of the effects of a decade of public belt-tightening that followed the financial crash. The poll suggests he turned traditional Labour-voting districts all over England his way.

The scale of the projected victory all but ensures that Parliament will vote to leave the EU at the end of January, ending a three-year political standoff over how and whether the U.K. should break with its biggest trading partner.

The larger the majority Mr. Johnson has, the greater leeway he will have in Parliament to steer future trade talks with the EU in any direction he chooses.

Mr. Johnson’s victory would mark the fourth consecutive defeat for the main opposition Labour Party, which hasn’t won an election since Mr. Blair took them to victory in 2005. After his second successive defeat, its 70-year-old leader Jeremy Corbyn is likely to face pressure to resign.

The final results of the election won’t be known for several hours. But if the poll is accurate, the vote would mark a remarkable turnaround for Mr. Johnson, who in the space of five months renegotiated a Brexit divorce deal with the EU and rallied his divided party and Britain’s exasperated voters behind it.

A majority of the projected size would allow Mr. Johnson to quickly push the withdrawal deal he negotiated with the EU through Parliament, allowing Britain to formally leave the bloc on Jan. 31