Britain’s new populist Brexit Party was on course to win the country’s European Parliament elections, according to early results released on Sunday, further roiling the already turbulent politics of a country polarized over its failed effort to leave the European Union.

Led by Nigel Farage, the Brexit Party’s strong performance humiliated the governing Conservatives, whose leader, Prime Minister Theresa May, on Friday announced her resignation after almost three troubled years in power.

The 28 member countries of the European Union voted from Thursday to Sunday for the European Parliament, the bloc’s only directly elected institution, which has extensive powers over legislation. The individual country votes often serve as a gauge on important domestic issues.

[See the results of the European Union elections.]

The results in Britain were a striking success for a party that has existed for only a few weeks, and for Mr. Farage, the campaigner for British withdrawal from the European Union. He is one of the country’s most divisive politicians but also one of its most effective communicators.