Academy puts on a trade fair, but without the price tags

In 1998, with the "Sensations" exhibition, the Royal Academy opened its doors to cutting-edge art and, at a stroke, transformed its image from that of a fusty, dusty, 18th-century institution to that of an organisation that lived in the world of the late Nineties.

In 1998, with the "Sensations" exhibition, the Royal Academy opened its doors to cutting-edge art and, at a stroke, transformed its image from that of a fusty, dusty, 18th-century institution to that of an organisation that lived in the world of the late Nineties.

Two years ago it tried to repeat that exercise with "Apocalypse", another blockbuster of a title. Chapman Brothers apart, that show made less impact than its predecessor – there was much less retching and raging in the aisles. No excitingly new talent emerged of the likes of Ron Mueck.

Now it seems something similar is being attempted with The Galleries Show, curated yet again by the exhibitions secretary, Norman Rosenthal, with the able assistance of Max Wigram. Or is it? Yes and no.

The purpose of this show is in part pedagogical. Over the past 10 or so years, the London gallery scene has undergone a mighty transformation. A decade ago you would have been hard pushed to find 10 galleries with an international reputation in London. Now there are 40.

This show sets out to demonstrate what 20 of the best offer. Each is given its own space within the Royal Academy. Some occupy rooms; others carve awkward shapes out of rooms. It is a world of small, self-sufficient kingdoms.

Does this mean it is a trade fair? Well, sort of, except that there are no price tags on any of the works. Of course not. That would be far too indiscreet. There were plenty of gallery owners about when I strolled through, and lots of artists too.

I asked Max Wigram what was the show's purpose. "What we are trying to do is to show what an important role galleries play in the London art world," he told me. "They're a huge asset, much underused, and much more important than museums. In New York people are accustomed to taking in a couple of galleries at the weekend, but here people are still afraid to walk in, afraid the gallery will expect them to buy something.

"The galleries represented here are open and free, and the artists, Japanese, Brazilian, Spanish, German, are a cross-section of the best in the world."

And was this show free, too? "No , it costs £5. You see, we're not a publicly funded institution." The best in the world? That's something of an exaggeration. Some work in this enormously uneven show is good, much of it is dull, modish and second-rate.

The highlights can be found in the following galleries: Frith Street Gallery (see Marlene Dumas' works on paper, all those vulnerable, knock-kneed nudes; and Thomas Schutte's massively buttocked "Steel Woman No9" in rusted steel). The Lisson Gallery is very strong, in an entirely predictable way: see the Deacon and the Kapoor, for example. Look out for Verne Dawson's brashly pleasing, magically realistic painting of the Olduvai Gorge at the Victoria Miro gallery.

And, most surprising of all in a show that is generally low on shocks and surprises, is the rotunda occupied by eight small paintings by Howard Hodgkin, now represented by the Gagosian Gallery. Hodgkin hasn't been seen in the Royal Academy for 20 years. Nor does he want to become a member. Perhaps Larry Gagosian knows a selling exhibition when he sees one.

The greatest disappointment is that Jay Jopling, London's most commercially successful gallerist, isn't here at all. Was Max Wigram sorry about that? "It's a pity. In fact, ... it's irritating ..." Why is he not here? "He has a new gallery space opening this month." But so has the Lisson, and it made it.