Whatever the motives of the 18-year-old German-Iranian who shot 10 people dead – including himself – in Munich on Friday night, Europe’s third violent attack on civilians in eight days risks further shaking an already fractured and fearful continent at a time when it least needs it.

German authorities said on Saturday it was premature to call the shooting in the Bavarian state capital a terrorist attack, and have uncovered no evidence that the teenage gunman, who had been receiving psychiatric and medical treatment, had links to any Islamist group.

Nor, police said, was there any apparent connection to last Monday’s train attack near Würzburg, in which a 17-year-old Afghan asylum seeker injured five people with an axe and a knife in an incident that the German interior ministry said was inspired by Islamic State.

But barely a week after Mohamed Lahouaiej-Bouhlel, 31, drove a truck through the Bastille Day crowds in Nice, killing 84 people in an attack claimed by the jihadist group, the French president François Hollande was quick to speak of a “terror attack” that “aims to foment fear in Germany after other European countries”.

And no matter what actually drove each assailant, Europe’s fast-growing populist, anti-immigrant and law-and-order parties – already riding high on anxieties fuelled by prolonged economic stagnation, a massive influx of refugees and migrants, and atrocities in Paris and Brussels that claimed 180 lives – plainly see electoral potential.

Marine Le Pen, the leader of France’s far-right Front National, reacted to the slaughter in Nice by accusing Hollande’s Socialist government of doing “nothing, nothing at all” to protect the country’s citizens, demanding it “declare war” on extremists and ensure the “total eradication” of fundamentalism.

Hours after the shooting in Munich, Christian Lüth, a spokesman for Germany’s populist, anti-immigrant Alternative für Deutschland party, said in a tweet which he subsequently deleted: “Vote AfD! Shots fired at the Olympia shopping centre: people dead in Munich. Police say there is an acute terrorism situation.”

A poll last week suggested Britain’s Brexit vote has boosted support for the European Union in leading member states, at least in the short term. But the uncertainty the referendum result has unleashed over the bloc’s future shape and direction has compounded a sense of long-held certainties fast evaporating.

Europe is turning increasingly inward. A survey last month by the Pew research centre in Washington DC found an average 56% of respondents – and a majority in seven of the 10 member states polled, which included Italy, Spain, France, Germany, Sweden, the Netherlands and the UK – felt countries should “deal with their own problems” before helping others.

Another poll this month found half or more of respondents in eight of the 10 countries felt refugees “increased the risk of terrorism”; in five, a clear majority believed refugees would “take away jobs and social benefits”. At least 25% in every country polled said they had a negative opinion of Muslims.

With key referendums and elections due in the next 12 months in Austria, the Netherlands, Germany and France, the distrust, disillusion and even full-scale rejection of the political establishment already evident across much of Europe – and that risks being further deepened by each act of violence – could rock the continent’s political foundations.

Almost everywhere, Europe’s traditional mainstream parties are in retreat, with centre-left social democrats and centre-right Christian democrats who have dominated national politics for 60-odd years struggling to command a fraction of the support they would have considered automatic even five years ago as voters increasingly doubt their capacity to address their problems.

In early October, Austria holds fresh presidential elections after the country’s highest court earlier this month overturned the veteran Green Alexander Van der Bellen’s knife-edge May victory – by just 31,000 votes – over Norbert Hofer of the far-right, anti-immigration Freedom party. In the first round, candidates from the main centre-right and centre-left parties barely reached 10% each.

The same month, Italy’s centrist prime minister Matteo Renzi risks his political future in a referendum on governance and constitutional reforms that, given recent mayoral triumphs by the Eurosceptic Five Star Movement and Renzi’s own plummeting popularity – down from 74% in June 2014 to about 40% – he is by no means sure to win.

October also sees a referendum in Hungary on a call by the hardline prime minister, Viktor Orban, to reject the mandatory refugee quotas demanded by Brussels as part of the EU’s desperate attempts to handle the migration crisis, while in March Geert Wilders’s anti-EU, anti-Islam, anti-immigrant Party for Freedom (PVV) looks on course to emerge as the largest political party in the Netherlands.

In France Le Pen, who – like Wilders – is also holding out the prospect of an EU membership referendum, is forecast to defeat a mainstream candidate and advance to the second round of presidential elections in May.

Even in Germany, Alternative für Deutschland – whose rhetoric has found a ready audience since the country opened its borders to 1.1m refugees last year, and which argues Islam is not compatible with the constitution – could, at its current 14-15% in the polls, end the two-party political stability that has lasted since the end of the second world war. Federal elections are due before October.