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John Sainsbury's philanthropic gift of £25m to the British Museum is very welcome <small>[see update below]</small>. The museum's director Neil MacGregor and the culture secretary Jeremy Hunt will be particularly pleased.

MacGregor is undertaking a piece of work for Hunt on the potential of philanthropic giving in the UK, in order to provide the minister with some arts-grandee-endorsed research to back up a widely-declaimed desire by the coalition government to increase individual charitable donations to the arts.

So securing one of the largest donations ever made in the country for his own institution is tantamount to handing in your homework early. But, other than it being quite a lot of money, the gift is unexceptional.

The Sainsbury family has been a generous benefactor to the arts for many years and is known to like capital projects - that is, new buildings - on which what are known as "naming rights" are available. Nor is the British Museum as beneficiary of such largesse remarkable.

The museum, the first national public museum in the world, was founded after an act of philanthropy. The physician, naturalist and inventor of drinking chocolate bequeathed in return for a £20,000 payment to his heirs. The deal was concluded in 1753, the year of Sloane's death.

Other recipients of Sainsbury money such as the Tate Gallery, the National Gallery and the Ashmolean museum were all founded on substantial philanthropic gifts. And they have continued to attract sizeable donations. According to Tate's Nicholas Serota, his institution will follow up the British Museum announcement with its own news of a multi-million pound individual contribution to the extension of Tate Modern in the near future.

These institutions form part of the upper echelons of the British establishment, which is where major philanthropists want to play and to be seen playing. The leaders of the institutions are routinely knighted, and add a great dollop of intellectual credibility at the drinks and dinner parties of the super-rich.

The directors of our major museums are expert fund-raisers who are all on first-name terms with the country's 20-or-so major arts-minded philanthropists. Although the urbane charm of each certainly helps ease a philanthropist's chequebook from attache case to desktop, it is the building he or she manages that is the real pull.

Having a Sainsbury Wing of the National Gallery, a great and globally respected institution, is always going to be more alluring to the donor than a Sainsbury Wing at say, the Watershed in Bristol.

And that's the problem. This latest gift will be pointed to as evidence that there is plenty of private money knocking about to prop up the arts in their time of need. And there is - if you are one of the very big boys. Not so if you're the avant-garde arts centre in South Yorkshire.

The artistic directors of regional theatres and galleries don't move in the same circles as the their knighted colleagues from the national museums. Nor do they run world-famous buildings on which a name could be engraved, or possess a back room of fund-raising staff to arrange private in-gallery tours and backstage meet-and-greets.

And it is likely to be those in "the regions" that are hit hardest by the forthcoming cuts. Take England: they are facing the prospect of their Arts Council subsidy being cut as well as their local government subsidy. Regional museums and galleries are also likely to see a reduction of their Renaissance in the Regions money, the central-government-funded programme of rejuvenation of tired buildings and working practices that has seen audiences grow by over 40%.

There is little prospect of these regional arts institutions raising 1% of John Sainsbury's recent gift to the British Museum - probably not even 0.1%.

But maybe they could, if they tried a new approach. What if, say, all the major regional arts institutions grouped together as one entity for fund-raising purposes: "The Arts Alliance"?

Between them, they could afford a decent fund-raiser or two who would work at the highest level and develop a fundable programme like Renaissance in the Regions, with naming rights available for a philanthropist. It would be of a size and scale to demand media and political attention.

Or such a central fund could be made up of lots of smaller donations, which might include a contribution from the national institutions. Nick Hytner, the National Theatre's artistic director, said recently that every director, producer and actor who works in his theatre had benefited from working in regional theatre.

So what if 5% of every ticket sale at, say, the National Theatre, British Museum and National Gallery went towards a regional fund? Or that these institutions used their vast footfall and reception areas to put out fund-raising boxes not only for themselves but for a regional fund too?

Update 14 September: I've been sent a note from the British Museum about how this story was reported across the media, which I'm very happy to append:

The Linbury Trust, a charitable trust established by Lord Sainsbury in the 1970s, has agreed a grant of £12.5 million to the British Museum to be paid over the next 3 years. Similarly the Monument Trust, a trust established by Lord Sainsbury's late brother Simon, has made a grant of £12.5 million to the British Museum, thus creating a combined gift of £25 million for the Museum's much-needed extension.