It is seen in Britain as a mere talking shop. The European Parliament usually makes UK news bulletins only when Nigel Farage hurls insults, Ukip MEPs literally fight among themselves or there’s another row about the Parliament’s costly travelling circus between Brussels and Strasbourg.

Yet the 751-member Parliament will play an important role in shaping Brexit and has the power to vote down any UK-EU deal. Although little-noticed in Britain, its influence has grown and most EU policies are now the subject of “co-decision” by the Parliament and Council of Ministers from member states.

The Parliament is already flexing its muscles over Brexit and taking a harder line than the European Commission, the EU civil service, and the European Council, the 27 national leaders.

A resolution backed by four political groups in the Parliament – the centre-right European People’s Party (EPP), the largest; the Socialists and Democrats; the Liberals and the Greens – says the European Court of Justice (ECJ) must police any long-term UK-EU agreement. That is incompatible with Theresa May’s pledge to end the ECJ’s jurisdiction in Britain.

The €64,000 question is: Would the Parliament dare to wield its veto and scupper a deal thrashed out by the EU and UK, which needs the approval of the Parliament’s constitutional committee and a session of all 751 MEPs?

The answer is probably no, since the MEPs will have a take-it-or-leave-it vote and will not be able to amend an agreement. If MEPs blocked a deal, they would almost certainly be throwing out protected rights for the 3 million EU citizens in the UK, which would not be a very good advert for their body.

In pictures: European parliament Brexit discussions Show all 12 1 /12 In pictures: European parliament Brexit discussions In pictures: European parliament Brexit discussions European commission member in charge of Brexit negotiations with Britain, French Michel Barnier listens at the President of the European Commission Jean-Claude Juncker speaking at the European Parliament in Strasbourg Getty Images In pictures: European parliament Brexit discussions Frank-Walter Steinmeier, President of the Federal Republic of Germany, delivers his speech at the European Parliament in Strasbourg EPA In pictures: European parliament Brexit discussions European Union's chief Brexit negotiator Guy Verhofstadt, President of the Group of the Alliance of Liberals and Democrats for Europe (ALDE), addresses the European Parliament during a debate on Brexit priorities and the upcomming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions Michel Barnier, European Chief Negotiator for Brexit reacts during a meeting at the European Parliament in Strasbourg EPA In pictures: European parliament Brexit discussions Member of the European Parliament and former leader of the anti-EU UK Independence Party (UKIP) Nigel Farage wears socks with Union Jack flag at the European Parliament in Strasbourg Getty Images In pictures: European parliament Brexit discussions Nigel Farage, United Kingdom Independence Party (UKIP) member and MEP, addresses the European Parliament during a debate on Brexit priorities and the upcoming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions European commission member in charge of Brexit negotiations with Britain, French Michel Barnier gestures during speeches at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions The President of the European Commission Jean-Claude Juncker (L) speaks with European commission member in charge of Brexit negotiations with Britain, French Michel Barnier at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions European Union's chief Brexit negotiator Guy Verhofstadt, President of the Group of the Alliance of Liberals and Democrats for Europe (ALDE), addresses the European Parliament during a debate on Brexit priorities and the upcomming talks on the UK's withdrawal from the EU Reuters In pictures: European parliament Brexit discussions Member of the European Parliament and former leader of the anti-EU UK Independence Party (UKIP) Nigel Farage gestures during speeches at the European Parliament in Strasbourg, eastern France, on April 5, 2017. The European Parliament will on April 5 lay down its "red lines" for negotiations over a Brexit deal, on which the assembly will have the final say in two years' time. / AFP PHOTO / Sebastien BozonSEBASTIEN BOZON/AFP/Getty Images Getty In pictures: European parliament Brexit discussions German president Frank-Walter Steinmeier delivers a speech during a plenary session at the European Parliament in Strasbourg Getty In pictures: European parliament Brexit discussions The European Parliament in Strasbourg, eastern France Getty Images

However, that does not mean MEPs will lack influence. It has already been felt. Brussels insiders believe the Parliament’s threat to scupper a deal if Britain imposed a cut-off date for EU citizens to enjoy UK rights on the day it triggered Article 50, helped persuade the Government to drop the idea. The cut-off will now be Brexit day in 2019, so any EU nationals coming to Britain before then would still be protected.

The Parliament will want to enjoy similar influence during the negotiations; its resolutions will be non-binding but will have to be taken into account. Its champion will be Guy Verhofstadt, the hyperactive former Belgian Prime Minister, who is never far from a TV camera or radio microphone.

As the Parliament’s Brexit co-ordinator, his mantra is that it is “better to have [Parliament] inside the tent pissing out than outside the tent pissing in”.

European Union's chief Brexit negotiator Guy Verhofstadt, who one Brussels source called "a pain in the arse" (Reuters)

The irrepressible chairman of the Alliance of Liberals and Democrats for Europe (ALDE), could be a thorn in both sides in the Brexit talks. “He is a pain in the arse,” said one Brussels source. “He will milk this for all it’s worth.” Another official described him as “the fly in the ointment.”

The Commission is alive to the need to keep the Parliament onside but the Council is worried about its growing attempts to muscle in on international negotiations. It has reined in Mr Verhofstadt by rejecting his attempt to join the EU’s negotiating team. Instead, he will attend its preparatory meetings.

Mr Verhofstadt, an arch-federalist, is no friend of Britain, which blocked his bid to become Commission president in 2004. So he is more likely to cause Ms May problems than her EU counterparts. Indeed, some MEPs say they will play “hard cop” to strengthen the hand of Michel Barnier, the EU’s chief negotiator, allowing him to play “soft cop” with the Brits

“He will say ‘I'm sorry, the Parliament won’t wear this, and it has a veto’ ”, said one EPP source.

The Belgian will matter more than Antonio Tajani, the EPP’s former Silvio Berlusconi ally who is now the Parliament’s president (and whom Ms May called on the day she invoked Article 50).

He has a lower profile than his combative predecessor Martin Schulz, who will be the Social Democrat (SDP) candidate against Angela Merkel in the German election this autumn. Mr Tajani, a pragmatist, gave Mr Verhofstadt a largely free hand on Brexit in return for his backing in the race to succeed Mr Schulz. Mr Verhofstadt withdrew his own candidacy, even though he could not have won.

Guy Verhofstadt addresses parliament ahead of vote on EU negotiation red lines

The hand of MEPs could also be seen when Donald Tusk, the Council’s president, set out the EU’s draft negotiating guidelines. They reflected the MEPs’ view that Ms May should be denied the sectoral deals she wants for financial services and the automotive industry; their calls for “substantial progress” on the exit agreement before a trade deal is discussed and a “level playing field” on competition and state aid.

Most MEPs see their role as standing up for Europe. Some would like to take revenge on a British government that has often derided them. Although the Parliament envisages an “association agreement” with the UK, MEPs are adamant that Britain cannot enjoy the fruits of EU membership outside the bloc and there is little conciliatory talk of a mutually beneficial deal. As Manfred Weber, who chairs the EPP group, said: “Only the interests of the remaining 440 million Europeans count for us. I don’t care anymore about the City of London’s interests.”

But the Parliament will not call all the shots. It will push a proposal by Charles Goerens, a Luxembourg Liberal MEP, that Britons who feel European should be able to opt in to associate EU citizenship after Brexit. This could allow them the right to move freely across the continent and vote in elections to the Parliament, which might appeal to some of the 48 per cent who voted Remain. But the Commission and Council do not see the idea as a runner. “A bit of grandstanding; it won’t fly,” said one insider.

Mrs May does have some friends in the Parliament. The European Conservatives and Reformists (CER) group, the third largest, which includes Tory MEPs, says it was not consulted about the four-party resolution and has drawn up its own blueprint. Syed Kamall, the group’s Tory chairman, who backed Leave, said the Parliament should avoid setting non-negotiable “red lines” for the negotiations. He said: “It must not be about winners and losers. A bad deal for one side will also be bad for the other.”