Guy Verhofstadt speaks during a European Parliament plenary meeting in Strasbourg | Patrick Seeger/EPA Brexit Files Insight Brexit warning: Forget the European Parliament at your peril If the Brits think EU leaders are inflexible, they could be in for a shock when MEPs get involved.

U.K. negotiators expressed mounting frustration this week over the seeming inflexibility of the leaders of the 27 remaining EU countries, who have insisted on settling Brexit divorce terms before discussing Britain's future relationship with the bloc.

But the EU's chief negotiator Michel Barnier offered up a pointed warning at the news conference Thursday wrapping up the latest round of Brexit talks. “I suggest that nobody underestimates the role of the European Parliament,” Barnier said — a reminder that MEPs wield a veto over any final withdrawal agreement.

While London may find the situation trying, dealing with the 27 leaders and Council President Donald Tusk could well turn out to be a picnic compared to the raucous 751-member Parliament. Some Parliament leaders, including its Brexit point-man, former Belgian Prime Minister Guy Verhofstadt, have taken a harder line on Brexit, and shown far less sympathy for the U.K.'s needs or wants.

In the latest of a series of outbursts that have made him something of a villain in the British press, Verhofstadt berated the U.K. in an op-ed in the Daily Telegraph, saying it had long enjoyed too much privilege and special treatment in the EU, and as part of its exit was seeking even more unfair advantage.

"U.K. ministers seem to want to devise a new customs union and seek to recreate all of the EU’s structures, in order to continue to benefit from the best elements of the EU, without it being called the EU," he wrote "This is not serious, fair or even possible given the negotiating time remaining — now significantly limited by the U.K.’s own decision to call a general election after the triggering of Article 50 [the treaty mechanism that set Brexit in motion]."

Verhofstadt is far from alone in the European Parliament when it comes to tough talk. In a statement Thursday, Gianni Pittella, the leader of the Socialists and Democrats group, slammed the U.K. for not negotiating in good faith.

"Beyond the goodwill expressed on paper, the U.K. government is far from being open and keen to have a serious discussion on the crucial points linked to the British withdrawal from the EU, citizens' rights, financial settlement and the Irish border," Pittella said.

He added, "How could we approach the discussion about our future relations if the U.K. is still reluctant to open dialogue about its financial commitments? The Tories bear total responsibility for the current stalemate, which risks badly affecting citizens and business."

Barnier, who served as a French MEP for several months in 2009 and 2010, is aware he needs to bring the Parliament with him and has carefully courted his former colleagues throughout the entire process.

He is a regular presence in the Parliament, including at plenaries in Strasbourg; he meets frequently with its leaders and the Parliament's working group on Brexit; as well as regularly briefing the Brexit steering group. On Tuesday, as negotiators dug in for the latest round of talks, Barnier met with the Parliament's president, Antonio Tajani.

Barnier knows that his elected former colleagues will have a decisive role to play in the withdrawal process: potentially torpedoing any deal. Anyone who forgets that — in London or Brussels — does so at their own peril.

This insight is from POLITICO's Brexit Files newsletter, a daily afternoon digest of the best coverage and analysis of Britain’s decision to leave the EU. Read today’s edition or subscribe here.