A meeting on Thursday heard that Brexit will also boost the ambitions of populist groups in other countries, such as France, Denmark and Hungary.
The UK decision to leave the EU has seen calls for similar referenda in several countries, including France, where Marine Le-Pen's far-right Front National has regularly polled highly.
Tanja Fajon, a Vice-Chair of Parliament's S&D group, told the meeting the referendum verdict reflected a "loss in public trust in politicians" and that this could now allow "nationalistic" groups to "dare to dream big."
"It will encourage and strengthen them to think that their countries might also leave the EU," said Fajon, who chaired the meeting.
The Slovenian MEP also noted that, since the result, there had been a big rise in racist and xenophobic incidents in the UK.
She said, "The radical right and extremists oppose everything and everyone that is different and my fear is that Brexit will further strengthen the rise of such extremism throughout Europe."
She also mourned the failure of the Remain side in the Brexit debate to counter the concerns about immigration on the Leave side.
"The Remain campaign clearly failed on this and this is the reality," she said.
Front National leader Marine Le Pen said Britain had begun a movement that cannot be stopped.
Europe's other far-right parties have rejoiced at the UK's vote to leave the EU, hailing it as a victory for their own anti-immigration and anti-EU stances and vowing to push for similar referendums in countries such as France, the Netherlands and Denmark.
In the Netherlands, the far-right and anti-immigration leader Geert Wilders called for a referendum on Dutch membership of the EU
In Athens, Golden Dawn, Europe's most violent right-wing party, rejoiced at the referendum result, predicting it would further empower "nationalist forces" across the continent.
The parliamentary meeting, organised by the S&D group, was called to debate ways of "countering radical right and xenophobic populism" in Europe.
Another speaker, Cas Mudde, professor of political science at the University of Georgia in the US, who highlighted the "transformation" of Hungarian Prime Minister Viktor Orbán, saying this should be of "particular concern" to the rest of Europe.
Mudde, who has spent 25 years studying the far-right, said, "He started out as a young, liberal reformer and was the darling of Europe. But his discourse and narrative is now similar to that of far right groups.
"Orbán has now put the far-right vision at the heart of his message about Europe. He has made anti-culturalism acceptable."
He condemned the EPP for "continuing to support" Orbán, saying this had emboldened the Hungarian.
Mudde, a Dutch national, also voiced concern about the rise and popularity of the far-right Danish People's Party and said that the rise of the far right was mirrored in America with the success of Donald Trump.
He suggested that the best way of countering the rise of far right populism was to regain the trust of the public.
"Social Democrat and other politicians have lost public trust and not because of the rise of such groups. It happened before they started to emerge. The only way of countering this is to regain public trust and that is something that will take time."
The meeting was told that as the continent struggles to deal with a refugee crisis and economic issues, some of these right-wing parties are gaining in popularity. These parties already have seats in their countries' Parliaments as well as seats in the European Parliament.
Alternative for Germany (AfD) was founded in 2013 as the EU struggled to bail out members hit by economic crises. The party's membership has grown to over 20,000.
After remaining on the fringes of mainstream French politics for over four decades, the National Front has emerged as an important political force in the past few years.
It stunned many in 2014 after winning 25 per cent of the vote in the European elections, which earned it 21 out of France's 74 seats in the European Parliament. The party is one of Europe's largest, with roughly 83,000 members.
The Freedom Party of Austria is an anti-immigration, anti-Islamic right-wing party almost won this year's elections in Austria. It was founded in 1965 and has a membership of over 50,000.
The Dutch Party for Freedom is an anti-EU, anti-Islam political party which has called for closing all Islamic schools in the Netherlands.
The party has also suggested recording the ethnicity of all Dutch citizens.
Jobbik, the Movement for a Better Hungary, is one of the most extreme far-right, radical nationalist parties in Europe.
Like most European far-right parties, Jobbik is also against immigration and says a "No Vacancy" sign should be put up along Europe's borders.