While the news in Britain is dominated by domestic politics and celebrity, Russian troops remain massed on the Ukraine border as nationalist confrontation escalates in eastern Ukraine. It's the most serious threat to world peace since the end of the cold war. The unacceptable policy on gay rights already unleashed by the Russian government now looks like a warning sign the world should have paid more attention to that something was seriously going wrong.

Perhaps you disagree that Vladimir Putin is the most dangerous man in the world right now – maybe you admire him like Nigel Farage does – but if I am right to be shocked and scared by Russia's current course, the question that follows is the one Lenin asked: what is to be done?

Matthew Bourne has just offered one answer by refusing to tour his gay Swan Lake to Russia. I believe a cultural boycott is in this instance a very good idea, and visual artists must join it. No more art for Russia until it returns to the democratic and peaceful road!

One reason this can work is that Russia really cares about art, music and literature. It has a great cultural tradition that is both truly popular and profoundly serious. I'll never forget the time I went to the Mariinsky theatre in St Petersburg to see (or is it hear?) Tchaikovsky's opera Eugene Onegin. The atmosphere was so much more passionate than at any British opera production I've been to.

It really is depriving Russia of something to refuse to tour an important production of the same great composer's Swan Lake there. Russia is a country that even in the depths of the second world war turned to classical music for solace, taking heart from Shostakovich's Leningrad Symphony. It is also a land that loves visual art. There is no greater museum on earth than St Petersburg's Hermitage, with its masterpieces that reflect the deep love of art by Russian collectors.

Great Russian art lovers such as Sergei Shchukin, who commissioned the Hermitage's modern treasure Matisse's Dance, have their heirs today in the oligarch collectors who do so much to fuel the London gallery and auction scene. In fact, financial dealings between Putin's Russia and the British art world go deep – just as in other businesses, the network of money intricately connects Russia's elite with British art. This gives artists, museums and art dealers a real way to make a difference – if they can face financial loss.

Anyway I've enacted my own boycott. I was asked to write about a Russian artist, for Russian money. I have refused and offended several people in the process. The point is not the artist – nothing against him – but the money. It is by refusing to turn Russian money into cultural capital that we can get the point across that Putin's policies are beyond the pale.

Or is that pompous? Is what we do in the west utterly irrelevant? I hope not. Russian culture, as Orlando Figes adeptly showed in his book Natasha's Dance, is not only intense and creative but torn between west and east, between European and Slav self-consciousness.

In his film Russian Ark, the director Alexander Sokurov celebrates the way Russia has preserved so much of the best of Europe in the Hermitage. A boycott that cuts off those western cultural connections is a genuine threat to this cultured country. Refuse the oligarch money, art world. You have nothing to lose but your bank balances.