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Here at last ... a visitor looks at Matisse's Dance at the Royal Academy. Photograph: Cate Gillon/Getty

The From Russia exhibition that opened this week at the Royal Academy only narrowly escaped disaster. It was not until January 9 that the Russian government gave its consent for the paintings to visit England. With the catalogue at the press and no substitute exhibition on the stocks, cancellation could have bankrupted the RA.

What was the problem? The show explores the relationship between French and Russian art between 1870 and 1925, and includes the superb collections of the 19th-century Moscow merchants Sergei Shchukin and Ivan Morosov, which were nationalised at the Russian revolution in 1917. Their paintings are now in the Pushkin Museum, Moscow, and the Hermitage Museum, St Petersburg - the collections were divided after the second world war. From time to time their heirs have attempted to get them back, and have taken the opportunity of the paintings appearing abroad to claim them. The Russian government was afraid they would do it again.

Following the RA's announcement of the exhibition in October, British press coverage stressed that the Shchukins and Morosovs might once again seek to reclaim their assets. While there were already safeguards to prevent this, the reports worried the Russian government, which began to ask for extra guarantees. It has been widely assumed that the difficulties result from the deterioration in diplomatic relations following the Litvinenko murder, but I am assured this is not the case. As Secretary of the UK Friends of the Hermitage I have had a ringside seat. Only when Culture Secretary James Purnell responded to a cry for help from the RA and brought the enactment of new protection from seizure legislation (Part 6 of the Tribunals, Courts and Enforcement Act) forward to December 31 was the crisis defused.

Immunity from seizure has become a central concern of the world's great museums in recent years. Restitution is in the air: art that disappeared at the time of the Holocaust, treasures unearthed by tomb robbers and illegal excavators, as well as art removed from original owners by revolutions and wars, are being reclaimed on all sides. Museums fear that by loaning works for exhibition abroad they may lose them. Yet the sharing of art among different nations through travelling exhibitions has enormous cultural benefit. Great art belongs to the whole world, and culture should have no frontiers or exclusion zones.

Battles over Shchukin and Morosov's pictures have helped embody these principles in law in country after country. In 1954, when 34 of Shchukin's Picassos were exhibited in Paris, his daughter Irina went to court to claim them. The paintings were rushed to the Russian embassy where they had diplomatic protection and came quietly home. In 1993, her son - Shchukin's grandson - went to court to claim Matisse paintings on loan to Paris's Pompidou Centre; the judge ruled that even in France, ownership was determined by Russian law since France had officially recognised the Soviet government.

The Shchukin and Morosov exhibition in Essen, Germany in 1993, which included a reconstruction of Morosov's music room with its specially commissioned wall paintings, helped clarify German law on this issue. Then in June 2000 Irina Shchukin's son, André-Marc Delocque-Fourcaud, filed suit in Rome to seize Matisse's La Danse, on exhibition in a sensational display of Shchukin and Morosov pictures from the Hermitage at the Quirinal Palace. He left his challenge until the last days of the exhibition and when the Hermitage heard of it from local newspapers the paintings were packed and shipped home with unprecedented speed.

The real watershed came in November 2005, when trucks containing 55 Impressionist paintings from the Pushkin Museum were held at the Swiss border at the request of a trading company called Noga, which claimed that the Russian government owed it $25 million and much more in damages. The paintings - including Monets, Renoirs, Sisleys and Van Goghs - had an insurance valuation of around $1 billion but the Swiss Appeal Court ruled that Noga had no right to sieze them. However, Professor Mikhail Piotrovsky, director of the Hermitage, threatened to recall all the art works the museum had on loan around the world and cancel exhibitions unless proper guarantees were available. The Dutch government moved swiftly to adjust its procedures since a new Hermitage museum was planned in Amsterdam, and for the first time Britain began to take the issue seriously.

The director of the British Museum, Neil MacGregor, and the director of the Courtauld Institute, Deborah Swallow, gathered their museum colleagues to lobby the government. Piotrovsky was invited to a meeting by the then minister of culture, David Lammy, to explain his concerns. Everyone relaxed a little after the Treasury Solicitor's office discovered that there had been legislation on the books since 1978 that protected state-owned property from seizure in Britain: Russia's major museums are all state-owned. However, new legislation was considered necessary to protect private loans. This was on its way in October when the Royal Academy announced its exhibition.

It is sure to be a blockbuster. Meanwhile, the heirs of Shchukin and Morosov have issued a statement calling for "an agreement that reasonably compensates and pays a percentage of the material benefits that accrue from the exploitation of the works". They face a struggle. It has been shown over and again, and around the world, that people hold culture above private property in the scale of human rights.