In 2016, as Theresa May sought to demonstrate her Brexit credentials, she mocked the tendency of some high-minded liberals to describe themselves as “citizens of the world”. A better description, she observed acidly, would be “citizen of nowhere”.

Not long afterwards, Orlando Figes, whose mother fled Nazi Germany in 1939, tweeted that he had decided to become a German citizen “bec [sic] I don’t want to be a Brexit Brit”. Presumably, he then returned with renewed urgency to complete this impassioned 576-page account of how European culture broke down the borders of the mind in the 19th century. A project he had worked on for years had suddenly become a symbol of resistance to the new nationalism.

Meticulously detailed, exhaustively researched and written with Figes’s characteristic verve, The Europeans: Three Lives and the Making of a Cosmopolitan Culture is a sweeping tour de force and a monumental work of historical synthesis. Focusing on the intertwined biographies of a famous French opera singer of Spanish descent, her French impresario husband and one of Russia’s most beloved novelists, Figes traces this trio’s fluctuating fortunes, zooming out from time to time to investigate subjects such as the middle-class craze for piano-playing and the birth of the travel guide.

We first meet Pauline Viardot, one of the great sopranos of the mid-19th century, as she prepares to sing Rossini at St Petersburg’s Bolshoi theatre in November 1843. Accompanied by her husband, Louis, she travels to Paris, a journey made a great deal easier by the opening of the first international railway, from Antwerp to Cologne. It is a sign of things to come.

The 19th-century equivalent of the medieval cathedral was the city concert hall and the theatre.

The rise of the railway, combined with new methods of printing and photographic reproduction, mass communications and new laws of international copyright created an unprecedented boom in the arts. Singers, musicians and actors crisscrossed the continent to satisfy the booming demand. Emerging national newspapers and regional press ensured that their reputations preceded them.

“From the very start,” writes Figes, “the railway weakened national frontiers... and powered the international circulation of European music, literature and art.”

Culture, for so long the province of aristocratic elites and closed circles, was opened up to the newly mobile middle classes, who poured into towns and cities in search of entertainment. The 19th-century equivalent of the medieval cathedral was the city concert hall and the theatre.

In mid-19th century Russia, the mania for Italian opera was at its height. Viardot, not a conventional beauty but charismatic and possessing an extraordinary vocal range, was the diva most of Europe wanted to see. In St Petersburg, night after night, the youthful aspiring author, Ivan Turgenev, took his seat and fell in love with her. Travelling to be with Viardot in France and Germany, Turgenev spent much of the rest of his life at Viardot’s side and was rumoured to be the father of one of her four children.

The writer Ivan Turgenev. Photograph: Culture Club/Getty Images

Though the depth of his feelings was never quite reciprocated, he remained loyal. The easygoing Louis, considerably older than Pauline, seemed happy enough with the unorthodox arrangement.

This unofficial menage a trois presided over salons in Paris, Baden and then London. Figes offers walk-on parts for a who’s who of the European arts scene: the Schumanns, Clara and Robert, come across as hard work, bitterly lamenting Viardot’s lack of seriousness when she turns down the opportunity to perform in Robert’s new oratorio. Chopin, Brahms and Liszt come and go.

Berlioz falls unhappily in love with Pauline for a while, reflecting sadly that if he were a writer, he could explain the depth of his feelings. Charles Dickens weeps at her performance of Orphée in 1862 at Paris’s Théâtre Lyrique. Eyes still wet, the great author is taken to the diva by the impresario Léon Carvalho, who introduces him with the words: “Madame, je vous présente une fontaine!”

In Baden, where Turgenev and the Viardots build neighbouring villas, Fyodor Dostoevsky embarks on a catastrophic gambling spree and accuses his fellow author of betraying Russia by setting up home among German “thieves and swindlers”. Wagner, meanwhile, is a coming force, fiercely at odds with the cosmopolitan spirit of the age and seeking to establish a home for pure German art in Bayreuth.

By the late 19th century, the most famous European artists were feted and celebrated to an extent that, in some cases, they succumbed to a certain hubris. Not without relish, Turgenev recorded a conversation with a magnificently pompous Victor Hugo in 1875: “‘We were chatting about German poetry. Victor Hugo, who does not like people talking in his presence, cut me short and began to give a portrait of Goethe. ‘His best work,’ he said in an Olympian tone, ‘is Wallenstein.’

“‘Forgive me, dear master,’ (Turgenev interjected). ‘Wallenstein is not by Goethe. It is by Schiller.’

“‘It matters not. I have read neither Goethe nor Schiller, but I know them better than those who have learned their works by heart.’”

Hugo would have been gratified by the spectacle of his own funeral in Paris in 1885, which attracted 3 million mourners and saw his coffin placed under the Arc de Triomphe. But it is Turgenev who embodies the cosmopolitan liberal spirit that Figes wishes to celebrate. As a young man, he completed his studies in Berlin, immersing himself in European literature. As his complicated love life developed and kept him on the move, Turgenev acted as a peerless cultural intermediary, introducing Tolstoy and Tchaikovsky to western capitals and Flaubert to the Russians. He translated the Frenchman’s works himself, so fastidiously that Flaubert complained he was taking too much time to finish the job.

Turgenev began writing Father and Sons on the Isle of Wight, annoying both radicals and conservatives in Russia, and was briefly imprisoned by the tsar for the searing indictment of serfdom contained in his Sketches From a Hunter’s Album. He told the incandescent Dostoevsky that he considered himself “a German, not a Russian, and am proud of it”. But he was buried in Russia amid extraordinary scenes of mourning.

If anyone stood for what Figes describes as “a Republic of Letters based on the Enlightenment ideals of reason, progress and democracy”, it was Turgenev. A citizen of the world, one could say. And the hero of this remarkable tribute to the artistic pioneers of the European ideal.

• The Europeans: Three Lives and the Making of a Cosmopolitan Culture by Orlando Figes is published by Penguin (£30). To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99