With less than two months to go before £50 million must be raised to save one of Titian's greatest masterpieces for the nation, there is cautious optimism that the target can be reached. Despite the fact that there is still a huge financial gap to be bridged, the directors of the National Galleries in London and Edinburgh have been encouraged by support from virtually every artist of note in Britain - and by hundreds of cheques sent in by members of the public.

They believe this evidence of widespread backing for the campaign, has strengthened their hand as they go into final negotiations with governments north and south of the border, as well as with funding bodies on both sides of the Atlantic.

Later today the artist Tracey Emin will deliver a letter to 10 Downing Street bearing the signatures of 39 artists, including the revered German modernist, Gerhard Richter, appealing to the Westminster Government to help to fund the purchase. The SNP administration in Scotland has announced that it will step in to help, though it has yet to announce the scale of its contribution.

Whatever he decides to do in response, Gordon Brown may feel it worth hanging onto Ms Emin's letter - it could be a work of art in itself. Bearing a reproduction of Titian's painting Diana and Actaeon, on exhibition at the National Gallery in London, it is likely to have a Tracey Emin original added on to dramatise her appeal. Her letter repeats the wording of a previous one, sent to The Times and signed by 60 leading artists, adding: “We also believe that in challenging times the heritage of the past and the art of the present are more important than ever.”

The money must be raised before the end of the year. The Duke of Sutherland, who owns several of the greatest masterpieces in the collection of the National Galleries of Scotland, has announced that he intends to sell two Titians - Diana and Actaeon, and its sister-painting, Diana and Callisto. He has offered first refusal to the National Galleries in London and Edinburgh for £100m - less than half their market value - which would allow him to take advantage of tax benefits. The galleries have until December 31 to raise £50m for Diana and Actaeon, which will also buy four more years to raise further funds for the second painting.

Officials at the Department of Culture, Media and Sport (DCMS) who are lobbying the Treasury for support are having to confront the fact that the campaign to save the paintings has been made considerably harder by the global credit crunch. At a time when jobs are being lost across the country, there is no great enthusiasm within government for forking out to save an Italian painting.

There is no money available in existing budgets following the spending review, and any assistance will depend on a special Treasury grant. No decision is expected before December, and the size of any funding will depend on support from elsewhere. “There will be no grand extravagant gesture,” said a DCMS official.

Despite this, the galleries believe that the money is “gettable.” An early commitment of £1 million from the Art Fund has helped, and they have put in a major application to the lottery-backed National Heritage Memorial Fund. In view of the financial crisis, however, a decision was taken to scrap a high-profile lobbying campaign planned for October, and rely instead on raising public awareness by using leading artists as “ambassadors” for the cause. The support from the public has buoyed their optimism. Cheques have been pouring in, including one for £52.49 - exactly half one pensioner's weekly earnings. There have been fundraising events across the country, lectures, guided tours for schools, even “celebrity-spotting” events at art galleries.

“We never expected such a wave of public support,”said the director of the National Galleries of Scotland, John Leighton. “When we made the announcement we knew it was big news, but we weren't prepared for this level of interest. It's very heartening.”

The galleries are expecting to make an announcement about the money they have raised within a fortnight.

Mr Leighton added: “I am optimistic that our target is achievable. It requires a huge collective effort but I am confident that it can be done.”

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