Has any museum or gallery ever been placed in such an appalling predicament? Not only has John Leighton, director-general of the National Galleries of Scotland, got to find £50 million in only four months for Diana & Actaeon, one of Titian's masterpieces, but he has to find another £50 million in four years to buy its pendant, Diana & Callisto. If not, they and some 20 other pictures in the Duke of Sutherland's collection, undoubtedly the finest Old Masters in private hands, may be lost to Scotland.

Quite a facer for the federation of galleries in Scotland - the equivalent of the Tate and National Portrait Gallery, with added responsibility for sculpture and prints and drawings. How are Leighton, his chairman and his doughty trustees to succeed when their total annual purchase grant is about £1.25 million? Indeed, have they a snowball's chance in hell? I spent the best part of 28 years directing first Manchester City Art Galleries and then the National Galleries of Scotland and, with sickening regularity, I and my team were confronted with similar dilemmas, albeit on a much more modest scale.

I don't envy Leighton his present task. It is understood that these paintings, considered by the artist as a pair and never separated in their long and distinguished history, have been valued at a little under £150 million each. They are “exempt” items (death duties have been deferred) hence the nation can buy them at a vastly reduced price. The “market” price is adjusted by a complicated formula which provides an attractive douceur to the private owner to sell to a public gallery; £50 million each seems a snip. But we are entering a recession, the Treasury is under constant pressure and considerable sums of money, otherwise available to the Heritage Lottery Fund, have been transferred to the London Olympics.

Clearly, these sums are too large for Scotland to raise on its own. There has to be a partnership and our colleagues at the National Gallery, London have been wonderfully accommodating. Abandoning other projected acquisitions, they have agreed to join Scotland in this appeal to raise £25 million apiece and, if successful, will have a joint share. The key figures in London are Nicholas Penny, the new director, and Mark Getty, the new chairman (his father, Sir Paul, supported many national appeals). Both boards will try to persuade the Treasury, the Heritage Lottery and Heritage Memorial Funds to help. Inevitably they will have recourse to the Art Fund, which spearheaded the successful appeal to acquire The Death of Actaeon by Titian for the National Gallery, London.

Whatever the shortfall is, Leighton and Penny will be going out with their begging bowls, like a couple of mendicant friars. Inevitably, they will approach their old faithful sponsors and benefactors first, but the task is far from straightforward. Scotland has just bought the D'Offay collection of contemporary art in association with Tate Modern, and it is also involved in fund raising for the redevelopment and modernisation of the Scottish National Portrait Gallery.

The National Gallery, London also has important commitments. Both galleries will have to approach the various private grant-giving trusts but, above all, they must keep the appeal in the forefront of the public's imagination. By doing this not only will they attract welcome smaller donations, but also, conceivably, large sums from undreamt-of donors.

The threat of export of great works of art is a perennial one. The current system is inadequate and should be looked at again. New fiscal measures were suggested by the Goodison review five years ago, but these were never implemented.

So where do we go from here? We cannot risk this as a test case. The threat will not go away and the plight of the Titians and, in the long term, the rest of the Sutherland Collection, now demands resolution. To go down Italy's track of simply banning all exports of works of art of any age or quality, would be seen as monstrously interfering with the rights of private ownership. The Italian system leads to extreme secrecy among private owners, suspicion and often outright hostility between owners and curators and, above all, widespread smuggling. The alternative to this old Fascist solution was the Soviet one of mass confiscation - certainly a great way to build collections.

America offers huge tax advantages to both owners and donors. Most British owners have usually already been advised on avoidance of capital gains tax and capital transfer tax. They would, however, be tempted by the American system of credits against income tax. The French have recently introduced a variant of this system, which is not only seen to be fair but greatly benefits the French museums.

I hate to add yet more misery to the Chancellor of the Exchequer. He should look into the French system and introduce a British version as a matter of urgency.

Sir Timothy Clifford was director-general of the National Galleries of Scotland from 1984 to 2006

Times Recommends

• Paralysed while the Hamas hydra lives
• Wanted: a superhero to save America
• Blind faith in experts fails justice