When, during a press conference in Brussels the night after the Brexit vote, European Commission President Jean-Claude Juncker was asked whether the Leave victory heralded the eventual break-up of the European Union, his answer was an emphatic: "No".

Despite his confidence, enthusiastically received, a pertinent potential consequence of Brexit could be the opening of a eurosceptic Pandora’s Box, leading to continent-wide destabilisation of the European project.

As predicted, within hours of the Brexit verdict, France’s National Front leader Marine Le Pen and Dutch eurosceptic political leader Geert Wilders were demanding in-out referendums in their own countries. As EU leaders work out the terms of Britain’s exit from the EU, they will be watching eurosceptic parties in other EU countries with unease.

For disappointed British Remainers, the overall health of the EU is highly important. Further disruption and uncertainty will be harmful, especially for vulnerable people such as migrants, refugees and the unemployed. Consequences have already hit the UK in the form of an economy contracting faster than it has since 2009 and a spike in the reporting of hate crime (while an increase in reporting is positive, the particularly vindictive nature of some of the post-referendum incidents, such as Polish people receiving flyers calling them "vermin" in the post, can only point towards the legitimising effect that Brexit has had upon people harbouring latent xenophobic views).

The EU will have to act to avoid such problems worsening in Europe itself.

Eurosceptic parties are politically diverse; not all want to replicate Brexit and some should be welcomed as part of the continent-wide discussion about the future of the EU. Those that do favour departure, buoyed by the UK Leave vote, will be more confident and persistent in calling for referendums. Many are outright anti-immigration or Islamopohbic, two issues that need to be explicitly addressed by the EU and national governments.

Here is a run-down of European eurosceptic parties, most of which would like to follow the UK out of the European Union:

France

The National Front

Leader: Marine Le Pen

MEP count: 21/74

Political affiliation: Far right

France’s answer to Nigel Farage, Le Pen has worked to bring her party into the mainstream since taking over from her more divisive father in 2011. Strictly anti-euro, anti-immigration and frequently seen as anti-Islam, Le Pen once likened illegal immigrants to a "tsunami", and believes that French citizenship should be "inherited or merited", a platform upon which she ran her 2012 bid for the presidency. An EU referendum will almost certainly be proposed as a part of her 2017 presidential campaign.

Anti-EU federalism is on the rise in France, with Laurent Wauquiez, vice-president of the opposition Republican party calling for an end to the European Commission, in order to devolve powers back to member states. With such views circulating around the political mainstream, Le Pen is in a good position for the 2017 election. This is especially true following the NF’s record-breaking win at the regional level last December, in which 6.8m votes won 356 of the 1,758 available councils.

A recent Pew Research Centre survey indicated that 61 per cent of French people view the EU negatively, suggesting a strong appetite for a referendum. Whether Le Pen wins next year or not, the NF pose a formidable threat to France’s future in the European Union and social cohesion more broadly.

Finland

Finns (Previously The True Finns)

Leader: Timo Soini

MEP count: 2/13

Political affiliation: Economically left wing and socially conservative

This party's belief is that immigration should strictly be for the economic benefit of Finland, and that refugees should be relocated to countries bordering their home countries. This suggests that they would take exception to any EU quota-based refugee relocation programme. The party believes in a strong welfare state, but one that should be for the exclusive benefit of the Finnish people, particularly singling out Finns of Swedish origin as people who should be barred from national benefits. The idea of benefit restrictions on migrants echoes the sentiment behind David Cameron’s proposals to restrict access to welfare for EU citizens in the UK before they had worked for a certain number of years in Britain.

The Finns party has been historically marginal, but won 38 (out of 200) seats in the 2015 parliamentary election, capitalising on angst following proposals to bail out poorer southern countries suffering from the 2008 downturn. Although smaller and not as menacing as Le Pen’s party, the Finns could continue to fan the fire of anti-immigrant populism. Whether they are right or wrong about the EU, more xenophobic sentiment is certainly not what Europe needs at this time.

The Netherlands

Party for Freedom

Leader: Geert Wilders

MEP count: 4/26

Political affiliation: Far-right

The Party for Freedom is capitalising on fears from the rapid changes that have come about in the Netherlands as a result of progressive social and immigration policies. Although the PFF currently has only a small stake in government, it is due to increase its representation at the general election next March, and a poll conducted by Peil.nl suggests that it would take up to 44 seats in the national parliament.

Leader Geert Wilders is an incendiary figure, whose rhetoric is more aligned with that of Le Pen senior, rather than Nigel Farage’s blokey "common sense" approach. Wilders has called for a ban on the Koran, comparing it to Hitler’s autobiography Mein Kampf, and his party supports a Dutch ban on the burka and Halal meat. Although there is no equivalent of an EU-sceptic Tory party in the Netherlands, the PFF will try and increase its appeal by capitalising on terrorism in Europe, such as the attacks in Nice, during the aftermath of which Wilders tweeted: "No more terror, No more Islam."

As a country with a centuries-old libertarian tradition of free-trade, many Dutch people are instinctively cautious of the EU moving towards becoming a trade cartel, as Farage called it in a BBC interview in June. If the UK manages to retain access to the open market, avoiding World Trade Organisation tariffs, while gaining an exemption from freedom of movement, Wilders will be in an even better position to argue his case.

As a poll in June revealed that 54 per cent of Dutch people want to have an in-out referendum, the Party for Freedom will be closely watching the Brexit negotiations to see how it can best spin them to its advantage. Given its blatant Islamophobia, the PFF may help to legitimise and harden the softer Islamophobia present in France’s National Front.

Denmark

Danish People’s party

Leader: Kristian Thulesen Dahl

MEP count: 4/13

Political affiliation: Anti-immigration, economically liberal

Despite Denmark’s popular image as a socially progressive society, in the 2015 elections the right wing DPP became the second largest party with 21.1 per cent of the vote. The DDP is staunchly anti-immigration and anti-euro, opposing all notions of an "ever closer union". According to its website, the Danish People’s Party will not "accept transformation to a multiethnic society".

While its belief in free university education, health care and environmental stewardship distinguishes it from the likes of Ukip, its anti-asylum seeker proposals (including the deliberate delaying of family reunifications and permitting migrants' valuables to be confiscated by immigration authorities) places it far from the progressive eurosceptics of Spain, Greece or Italy. While it is not advocating an in-out referendum yet, given its powerful position in the Danish government and uncooperative response to the refugee crisis, it is certainly one to watch warily.

Italy

The Five Star Movement

Leader: Beppe Grillo

MEP count: 17/73

Political affiliation: Identifies itself as a populist, anti-establishment movement outside of the traditional left-right spectrum

Founded by ex-comedian Beppe Grillo in 2010, the party started as an exasperated protest against the corruption and cronyism of Berlusconi’s government. Since then, high unemployment, an economy smaller than pre-recession levels and direct involvement in the migrant crisis has led to frustrations being directed at the EU as well as Italy’s political establishment. The latter of these was crushed by the Five Star Movement in recent Italian regional elections, making member Virginia Raggi the first female mayor of Rome.

The Five Star Movement, unlike Italy’s right-wing Northern League, wants a referendum on membership of the Eurozone, rather than the European Union itself. However, as uncertainty mounts across Europe and the troubling north/south divide in Italy worsens, it will have to perform a balancing act between retaining popular, anti-establishment appeal and making tough decisions, which may push some members of the movement closer towards a full "Quitaly".

Given its support of progressive policies such as same-sex marriage, direct democracy and a tough stance on political corruption, the Five Star Movement’s voice is a welcome one in the debate on EU democratic processes. It will now have to prove itself capable of taking tough decisions and working in coalition in order to get its desired referendum on the euro, while resisting the nationalist Northern League’s wish for a full in-out vote.

The EU must listen

Our continental neighbours have first-hand experience of the refugee crisis, increasingly frequent terrorist attacks and now the financial doubt that Brexit itself is creating. Aware of this, eurosceptic parties are benefiting from a perfect storm of fear and uncertainty.

While further schisms may give rise to more puns – Frexit, Quitaly, Donemark, Portugone and so on – the threat of a domino Leave vote should be taken seriously. Populist campaigns are better-placed than ever to exploit fears about sovereignty, immigration and safety in order to distort facts and heighten tensions.

The fact that currently one-third of MEPs represent eurosceptic parties is indicative of a problem that cannot be ignored, practically or ethically. The low turn-outs at European Parliament elections, just 42.6 per cent on average in 2014, are reason enough to take eurosceptisim seriously.

Whatever one wants for the future of the EU, campaigns led by the National Front, the Party for Freedom or the Finns can only deepen divisions between us. Not all eurosceptic parties are bad news: genuine anti-austerity, pro-diversity voices such as Greece’s Syriza and Spain’s Podemos must be the counterweight to the democratic deficit in the European Union. These will counter narratives that reinforce social division and isolationism.

The EU must respond by listening to its citizens and responding to their concerns, particularly on the repatriation of powers from Brussels. This is something which, according to a recent report by Statstica, 42 per cent of Europeans want to see, versus only 19 per cent who favour further supranational centralisation of power. To limit Brexit contagion, and to create an organisation representative of its citizens, the EU must listen up.