WITH THE INTERNATIONAL art market attracting dizzying prices, Britain is losing the battle to prevent the exodus of its treasures. As the Tate and the National Gallery fight to stop a Reynolds and a Raphael from leaving Britain, the combined £41.5 million that they need to raise illustrates the size of the task.

Experts fear that many other masterpieces in private hands will emerge on to the market and be sold to overseas collectors because owners are noticing the vast sums being fetched. Museums and galleries with paltry acquisition budgets are unable to compete.

David Barrie, the director of the National Art Collections Fund, says: “We have seen a Rubens change hands for £50 million. It won’t be long before a painting reaches £100 million. Even the Getty Museum in Los Angeles is going to be stretched.

“With the great Old Masters, Impressionists and the Picassos, there are extraordinarily rich private collectors around the world who are able to compete for these high-cost masterpieces. Museums, galleries and the general public are the losers.”

To counter the losses, the Art Fund is lobbying for income tax relief on gifts of works of art to public institutions. The American example has proved that it inspires owners to donate works which museums could not pay for. Just as tax relief has recently been extended to gifts of shares and buildings, it should be applicable to art, Barrie says.

A report published this month by the Reviewing Committee on the Export of Works of Art says that, through a lack of funding, the system has “failed totally” to achieve its aims. In the past year, export licences on 31 objects worth £19 million were deferred to allow British institutions the chance to match the price. Those institutions managed to acquire 20 objects worth just £3.1 million. The report says that masterpieces are now “invariably exported” after the deferral period.

The National Gallery is trying to ensure that Raphael’s Madonna of the Pinks — “one of the great paintings of the world” — stays in Britain. That means raising £29 million to prevent the Duke of Northumberland from exporting it to the Getty Museum. Charles Saumarez Smith, the director of the National Gallery, says he is pessimistic about the future after Rubens’s The Massacre of the Innocents passed the £50 million barrier last year.

“The fact that it’s understood there were three private bidders for the Rubens is an indication that there are quite a number of private individuals with deep resources,” he says. The National Gallery receives “nought from grant-in-aid” for acquisitions. When Sotheby’s sold a Mantegna last week for £17.6 million, “we couldn’t even think of it”. The painting went to an anonymous private collector.

The Arts Minister, Baroness Blackstone, has this week offered a one-month export bar on the Raphael and a further six months “if necessary”. The National Gallery says it has already received many hundreds of donations and letters of support.

Among the nation’s most painful recent losses are two Michelangelo drawings. As the National Galleries of Scotland could not afford to match the £8 million paid by an American collector at Christie’s for The Risen Christ — one of his most beautiful pen studies of a male nude — an export licence had to be granted.

The Edinburgh gallery has again been unable to compete after Michelangelo’s Study of a Mourning Woman was rediscovered at Castle Howard in North Yorkshire.The work is due to go to an American collector unless £7.5 million can be raised. A decision on its future will be taken today. The export report notes that there is not a single drawing by this great master in a public collection anywhere in Scotland, Wales or Northern Ireland.

The Reynolds for which the Tate is fund-raising is Portrait of Omai, a depiction of the Tahitian brought to England on one of Captain Cook’s ships. His exotic looks and charm took society by storm in the 1770s. The masterpiece, also once at Castle Howard, was bought at Sotheby’s for £10 million by the London dealer Guy Morrison. Reports suggest he sold it to an Irish collector, John Magnier. An export licence deferral means that the Tate has until mid-March to raise £12.5 million.

The National Portrait Gallery is now awaiting news on a painting on a related subject — the Portrait of Sir Joseph Banks with Omai and Dr Solander by William Parry, a student of Reynolds. Banks and Solander travelled together as naturalists on Captain Cook’s first voyage to the Pacific in 1768. The gallery could not raise £1.8 million to buy it and the buyer who applied for the licence has failed to pay. The painting remains on loan to the gallery while the owner decides what to do with it.

The export committee’s report notes that, despite some successes, the long list of treasures lost over the past 50 years includes works by Rembrandt, Giulio Romano and Fra Bartolomeo.

• A feature about conservation in The Times last month inspired an anonymous reader to donate £28,000 to the Fitzwilliam Museum in Cambridge, enabling it to save an important 16th-century Flemish triptych depicting scenes from the life of the Virgin Mary.