Prime Minister Theresa plans to set in motion Britain’s exit from the European Union by the end of March. (Alastair Grant/AP)

The British people spoke in June: They want out of the European Union.

But more than five months after the country’s referendum, the question of who actually gets to pull the trigger on Brexit remains a muddle. Prime Minister Theresa May says she does. A high-level British court argued otherwise last month, ruling that Parliament must have a say.

Now it’s up to the U.K. Supreme Court, which on Monday began hearing arguments in a case that could complicate May’s plan to set in motion Britain’s exit by the end of March.

The case, one of the most constitutionally significant for Britain in decades, will determine whether May and her government can use a prerogative once reserved for kings and queens to invoke Article 50, the never-before-used mechanism for getting out of the E.U.

Her attorney general, Jeremy Wright, argued Monday before an 11-judge panel that the power is “not an ancient relic” but instead “a fundamental pillar of our constitutional state.”

The June referendum, Wright said, was conducted “with the universal expectation that the government would implement the result.”

Complicating that argument, however, is the fact that the referendum was not legally binding. The High Court for England and Wales said last month that Britain’s tradition of “parliamentary sovereignty” dictated that the nation’s lawmakers must be given the final say in any exit.

The outcome of the case — which will be argued through Thursday, with a decision expected next month — could have significant ramifications for May’s E.U. departure plans.

Unlike the public, which voted 52 percent to 48 in favor of getting out of the E.U., most members of Parliament prefer staying in the bloc.

Pro-E.U. lawmakers have been careful to insist that they have no plans to overturn the public’s will. But even so, a Supreme Court decision to place Brexit decision-making in Parliament’s hands could open the door to protracted negotiations even before Britain begins its two-year divorce proceedings with the E.U.

Shami Chakrabarti, legal affairs spokeswoman for the opposition Labour Party, told the BBC on Monday that Brexit “will happen, pursuant to the will of the people.” But she added that the party intends to use parliamentary debate to shape the final package.

“There is not a simple question of in and out of the European Union,” she said. “There are many questions that Parliament has to scrutinize about what happens next.”

A spokeswoman for May, speaking on the customary condition of anonymity, told journalists on Monday that opposition parties are trying to “frustrate the will of the British people by slowing down the process of leaving and trying to tie the hands of the government negotiation.”

The court case has reignited passions that have barely cooled since the June vote. After last month’s High Court ruling, British backers of E.U. membership celebrated while Brexit advocates condemned the judgment.

“Enemies of the People,” read the banner headline on the front page of the pro-Brexit Daily Mail. Above those words were photos of the three judges.

On Monday, rival protesters — some dressed as judges — staged small demonstrations outside the court. Brexit champion Nigel Farage had initially planned a 100,000-person rally on Monday in support of an exit. But he canceled those plans last week amid fears that it could lead to violence.

Read more:

Britain’s scientists are freaking out over Brexit

What a real ‘Brexit Britain’ would look like

Today’s coverage from Post correspondents around the world

Like Washington Post World on Facebook and stay updated on foreign news