On Saturday – exactly a week after the horrific attack in Pittsburgh – I had the privilege of attending a Shabbat service at a synagogue in London to show solidarity with the Jewish community, both here and around the world. We prayed for all those affected – the families, the friends and the wider Jewish community. This evening, I’m also proud to be speaking at the annual dinner of the Board of Deputies of British Jews – a great organisation that does an incredible job standing up for the Jewish community in our country.

Understandably, many Jewish Londoners – and Jewish communities around the world – are not only mourning the victims of the dreadful attack in Pittsburgh, but worried about what this means for their own safety. A synagogue should always be a sanctuary, a place where you feel safe to worship and practise your faith in peace.

The wicked terrorist attack targeted innocent Jewish Americans, but it felt like an attack on us all – on our way of life and on the freedoms we hold dear. The fight against antisemitism is not only about protecting the Jewish community; it’s a fight on behalf of everyone. For antisemitism is a threat to our values, to the cohesiveness of our communities and to our whole society.

Sadly, the rise in antisemitism and the far right can’t be treated simply as a passing trend. The Community Security Trust has reported that antisemitic incidents across the UK are at a record high, with the number of cases recorded in London alone rising by nearly 200% since 2011.

We know from our history that we ignore these incidents at our peril, and where antisemitism, left to fester, can lead. And we know from our history that an increase in antisemitism and rightwing extremism usually comes with a rise in other forms of hate crime and division – coinciding with a backdrop of economic hardship, nationalist populism and political uncertainty.

Facebook Twitter Pinterest ‘Politicians, in this country and around the world, must refrain from using the language of division to advance their political causes.’ Photograph: Frank Mattia/ZUMA Wire/REX/Shutterstock

Worryingly, all the warning signs are here again, so it is vital that we take action now.

In London, I’m doing all I can to fight antisemitism. Under my leadership, the Met police is taking a zero-tolerance approach to antisemitism, wherever it occurs. This includes within the Labour party, no matter how awkward others might find this. I’ve also set up a countering violent extremism programme at City Hall, which is working to stop the spread of extremist ideologies of all kinds.

But we must also encourage everyone, of all faiths and all backgrounds, to play their part in defeating this rise in hatred. This includes politicians, in this country and around the world, refraining from using the language of division to advance their political causes. Take the way President Trump is using immigration as a way to stoke up fear of migrants and to give credence to conspiracy theories ahead of this week’s US midterm elections. His is one of the worst examples in recent times of this kind of irresponsible and damaging behaviour.

It’s also been revealing how many people from the Jewish community in Pittsburgh have been critical of Trump following the attack – because they know that his rhetoric and actions in recent years have been facilitating the rise of the far right across the US, which has emboldened some who wish to sow the seeds of hate.

Depressingly, extreme views are now infiltrating the mainstream, with nationalist populist parties gaining strength in the US, across Europe and now in Brazil. We need to wake up to this threat from the far right and from the politics of blame and recrimination that’s seeping into our national debates.

A big part of any solution will be tackling the root causes of why more and more people are feeling left behind by globalisation, leading them to look to blame “the other” for their ills. But we must also take immediate action to mend the growing divisions within our society.

I’m proud to represent such a forward-looking, global city. On the whole, we don’t just tolerate differences in London, we respect and celebrate them. But we are still far from perfect – our communities have been changing rapidly and our sense of social cohesion is being put to the test as never before.

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One of the lessons from around the world is that a “hands-off” approach to social integration simply doesn’t work. And without action, the situation will only get worse. That’s why I believe one of the most important tasks now is to take proactive steps towards building stronger and more integrated communities. This means we need to start encouraging and facilitating greater social integration wherever we can – to strengthen social ties and bonds of trust between people of all faiths, races, ages and backgrounds.

There’s not going to be a quick fix to this problem: it’s one of the defining challenges of the 21st century. But I’m still optimistic that if we treat it with the seriousness it deserves, we can clamp down on antisemitism, stop the march of far right and nationalist populism and make a real difference in forging stronger communities – showing that hope, unity and love can always trump fear, division and hatred.

• Sadiq Khan is the mayor of London