BRUSSELS — There are some odd ducks in the 751-member European Parliament, plenty of ranters representing fringe parties and ascendant populists: Slovak neo-fascists, Greek Marxist-Leninists and French ultranationalists.

And then there is Britain’s Brexit Party, perhaps the most unusual of them all.

The 29 members of the Brexit Party in the European Union’s legislative body successfully campaigned for seats they say they did not want, in an organization they do not respect, in a political and economic union they intend to leave.

“I just hate it. I hate it more than I did before I was elected,” said Ann Widdecombe, a Brexit Party member in the European Parliament.

“There’s nothing useful or sensible about it,” said Widdecombe, who in her former life as a Conservative member of the British Parliament was best known for her opposition to fox hunting, abortion and gay rights. “I want to go home.”

But she’s stuck — trapped in a world of blond wood, modernist Mies van der Rohe replica chairs and signs in multiple languages.

And the Europeans are stuck with her and her kin.

E.U. leaders required Britain to hold elections for the bloc’s Parliament last spring as a condition for granting a Brexit delay. But the United Kingdom, unable to agree on how to exit the E.U., has had to ask for two more Brexit extensions since then.

So the British representatives are still here, like a vestigial wing of Westminster politics. The Brexiteers in Brussels say they will not abandon their seats until their mission, leaving Europe, is accomplished.

“We’re the naughty kids,” said Claire Fox, who decades ago was a leader of Britain’s Revolutionary Communist Party and is now a Brexit Party member of the European Parliament. “We’re here to make the Euroskeptic argument, to keep fighting the good fight for leaving.”

But they are not quite the true disrupters they believe themselves to be.

Their critics call them “furniture” — and worse. They are mostly mocked or ignored by their colleagues.

The Brexit Party — founded only last February by Euroskeptic radio show host and longtime European Parliament member Nigel Farage — bested both British Prime Minister Boris Johnson’s Conservative Party and the opposition Labour Party in European elections in May and has the most seats of any single national party in the 9th European Parliament.

In Brussels, though, to have any real clout, European Parliament members must belong to a group of like-minded legislators from seven of the 28-member nations.

The Brexit members have no allies, no veto, no power. They belong to no voting bloc, hold no committee chair, propose no legislation.

Outside the chambers, they are exiled to spartan offices, with a single aide each, in the far reaches of the Brussels compound. They idle away their time in buildings named after E.U. founding fathers — Altiero Spinelli, Paul-Henri Spaak — whom the Brexiteers confess they had never heard of before.

Mostly, they sit as members or as “substitutes” on committees, if they participate at all.

In debates, they get one minute to speak.

They try to make the most of it — for their YouTube videos, which can go viral back home.

In one session, the Brexit Party’s Martin Edward Daubney — a former tabloid newspaper editor who organized “straight pride” marches in London — compared Belgian politician Guy Verhofstadt to the “Darth Vader of Europe,” adding that “this place is his Death Star, where national democracy comes to die.”

The European Parliament likes to boast that it’s the only international assembly in the world where countries can vote for their representatives. Its lawmakers appoint E.U. executives, decide on the bloc’s budget and can approve or reject international agreements.

It has also earned a reputation as a dull, bureaucratic chamber, rubber-stamping legislation on when to apply manure to cow pastures.

But while there are many critics of the Parliament, and many Euroskeptics among its members, the Brexit Party often finds itself alone.

Brexit Party member Annunziata Rees-Mogg, whose brother Jacob is leader of the British House of Commons, intervened in one budget debate to compare the E.U. to England under the reign of King George III.

“Since the 1700s, it has been argued that there should be no taxation without representation,” she said. “I very much hope that this will be my final opportunity to speak in this democratic facade of a chamber.”

Heads were scratched. No one engaged.

In an interview with The Washington Post afterward, Rees-Mogg called the European Parliament “the most fake kind of democracy you could imagine. When you debate, you don’t debate. It’s all just pretend.”

At the Parliament’s opening session, the Brexit Party’s lawmakers stood and turned their backs during the playing of Beethoven’s “Ode to Joy,” the anthem of the European Union.

Fox said the demonstration was intended to make a point: that the E.U. “is not a nation, but has a flag, an anthem, a foreign policy and, maybe soon, an army.”

But afterward, she said, she and her party were disparaged as “pigheaded, ignorant, chauvinist yobs who didn’t know who Beethoven was.”

Telegraph columnist Michael Deacon wrote that it looked like the Brexiteers were “having the time of their lives” — while “their European counterparts . . . looked thoroughly traumatized. It was as if they’d been confronted by a coach-load of English football fans from the 1980s, hurling plastic chairs through trattoria windows, throwing up in public fountains, and chanting ‘Two World Wars and one World Cup’ with their tops off.”

The Brexit Party members of Parliament “aren’t frozen out, they’re ignored,” said Fabian Zuleeg, chief executive of the European Policy Center think tank in Brussels.

“Mostly, they’re no-shows,” he said. “They’re completely disinterested in the real work of Parliament.

“Farage? He’s accomplished two things. He’s promoted himself, and he uses his position to promote his cause, which is Brexit.”

Zuleeg noted that Farage has failed seven times to win a seat in the British House of Commons. But he has won five elections for European Parliament — most recently as a member of the Brexit Party, and before that as part of the UK Independence Party. “So it is the European Parliament that has given him his platform,” Zuleeg said.

It has given Farage an income, too.

The Brussels Brexiteers complain a lot about the “gravy train:” the salaries and perks doled out for European Parliament members.

The Brexiteers greedily slurp the gravy, say their critics.

Brexit Party members say they chafe at the chauffeured cars, the ample expense accounts, the long lunches and the low demands for most members, who are paid their per diems if they just show up.

Verhofstadt, the Dutch politician who leads the Brexit committee in the European Parliament, has countered: “The biggest waste of money in the European Union of today is the salary we all pay to Mr. Farage.”

Verhofstadt often trolls Farage — a buddy of President Trump — as a no-show showboat.

Members of the European Parliament make $9,700 a month before taxes and are entitled to a monthly $5,000 general expenditure allowance, which covers phones, computers and renting an office in their constituencies.

They also receive a flat rate of $350 daily to cover meals and hotels when they are in Brussels or Strasbourg, France — the Parliament splits its time between the two cities — and an additional $26,000 a month for staff salaries.

In interviews with The Post, Brexit Party members said they took the money.

“Why are we here? To give Westminster a kick in the backside to get on with it,” said Henrik Overgaard-Nielsen, a Brexit Party member of the European Parliament.

He is not a British citizen. He is a Danish dentist, longtime Euroskeptic, self-described lefty and resident of Britain, married to an English wife.

He credited the Brexit Party with weakening Theresa May when she served as prime minister and thwarting her half-in, half-out vision of Brexit.

“If it wasn’t for the Brexit Party,” he said, “we’d still have Theresa May as prime minister and still have her bad [Brexit] deal.”

In next month’s general election in Britain, the Brexit Party, which is unique in being registered as a private company and not a political party, could help deliver a mandate for a decisive Brexit. Or it could play the spoiler and produce another hung British Parliament, or even a victory for the opposition Labour Party — which could keep the Brexiteers in Brussels even longer.

“Get me out of this stupid job,” said Fox, the former communist.

After these few months sitting in the European Parliament, Fox assessed: “It’s deadly dull, technocratic. It’s politics with the guts ripped out of it.”

Plus, she said, “we’re not made to feel very welcome.”