Three thousand refugees now arrive in Europe every day, mainly heading for Germany. It’s hard not to feel uneasy – even fearful – about how German and European politics are going to evolve in reaction, and how this might affect the very future of the EU.

Paris might still be reeling from the 130 deaths in November’s terrorist attack, but now Germany is recoiling from the multiple attacks on women on New Year’s Eve from apparently young Arab men, many new immigrants or asylum seekers.

Terrorism can be dealt with by aggressive police, detection and surveillance work. The European public may not like the impact on their liberties, but they can recognise a feasible response is nonetheless possible. However, managing unreconstructed attitudes towards women by newly arrived young Arab men is far harder and much more menacing. It poses the question that a liberal society does not want to confront. Is cultural coexistence possible – and if not, what is to be done?

The German media, police and criminal justice system have been agonisingly slow to respond, perhaps hoping that silence would make the problem go away. But a week later, it is now becoming clear that there were ugly incidents on New Year’s Eve in many German cities. In Cologne up to 1,000 men, many described as of North African or Arab appearance, and aged between 18 and 35, gathered in the huge square between Cologne cathedral and the main railway station. They let off fireworks and robbed passers-by. Of the complaints, 117 involved sexual assault, including two allegations of rape.

Wolfgang Albers, Cologne’s police chief, who did not accept offers of aid from a nearby police force and issued a press statement on New Year’s Day saying that NYE had passed off peacefully, has been suspended by the state interior minister. The local public TV station, which did not broadcast any news for two days after the events, has publicly apologised. Only now are German newspapers and politicians beginning to engage with the profound issues.

Some of what is surfacing is pure poison. Police found a crib sheet on one of the detained men with phrases such as “great breasts” and “I want to f*** you” translated into German. Another is alleged to have told police that they couldn’t touch him because: “I’m Syrian, you have to treat me nicely. Frau Merkel invited me.” Fireworks were allegedly hurled at the cathedral as a symbol of Christianity.

No surprise that Julia Klöckner, the leader of Mrs Merkel’s CDU in Rhineland-Palatinate, said the attacks had been a wake-up call: “We really need to take off the blinkers.” No surprise either that the mayor of Cologne should be derided for advising women to keep men at arm’s length. Who is to blame for women being at risk? Women for simply being women?

The German chancellor is trying to steer a course. Recorded before the events in Cologne, her new year’s message to both her fellow German citizens and the refugees was to see the crisis as an opportunity. Germany needs millions of young qualified workers (more than half the refugees are highly skilled, it’s been said), allowing refugees to give to the society of which they wanted to be part. But, post-Cologne, she has begun to strike a different note.

“Women’s feelings of being at people’s mercy without any protection, is intolerable for me personally,” she declared. Her government is to review its refugee policy, with one likely initiative being immediate deportation for those convicted of any criminal activity. At the same time, Merkel is aware of the danger of surrendering to fear. “We must also keep talking about the basis of our cultural coexistence in Germany: people rightly expect that actions follow words.”

Meanwhile the extreme right has seized on events as proof positive that Germany must stop accepting refugees immediately or otherwise face an “impending cultural and civilisational collapse”, as the populist Eurosceptic Alternative für Deutschland puts it.

The initial slowness of response from both police and media was nothing to be proud of; equally feeding a political tradition whose antecedents Germans know and fear must be avoided.

Merkel will work for burden sharing and solutions to stop the refugees at source

So far what the Germans call the “Willkommenskultur” is still alive. Merkel and her SPD coalition partners will insist on the rule of law, getting tougher on deportation. There will be no talk of noxious multiculturalism, but instead of cultural coexistence in which the host society’s values are paramount. The German media will be more vigilant about honest-to-God reporting.

Abroad, Merkel will work for burden sharing, tougher measures to patrol Europe’s borders and seek solutions to stop the refugees at source – ending the war in Syria and persuading Turkey to host more people. Above all, she will look to the refugees themselves to do all they can to castigate and marginalise the minority who are inducing such a toxic reaction.

The British interest is unambiguous: Merkel must succeed, or a liberal Germany, and with it a benign European Union, will be lost. Already the venomous Hungarian leader Viktor Orbán is calling for tougher border controls, and the need to defend Europe’s values – code for an excuse for mass expulsion of refugees. He will have a new hearing in parts of Germany.

Amid this growing turmoil, the assumptions on both sides of the referendum debate are complacent and rest on Britain needing to do nothing to shape its continent. The pros insist that Europe offers us a great deal, while sceptics claim we can leave and still trade with an open, free-trade Europe. Britain, in or out of the EU, can use it as a milch cow. Good old liberal Germany will continue to anchor everyone.

It may not. What is being asked of Germany is enormous: it is to their credit that Germany’s leaders accept it – and to the public’s credit that so far it has stood behind them. But the latest poll in Germany for the first time reports a majority in favour of closing Germany’s borders. More Colognes, and that figure will grow further.

Yet this is a common European problem. It would be magnificent if a leading British politician would make the case for sharing Merkel’s objectives, and give her and her people a sense that we are with them – working to the same ends with the same mixture of realism and idealism. I bay at the moon.