The nation's paper fortune: Drawings from the British Museum collection

The British Museum is showing some of its superb collection of drawings by the masters of modern art. Adrian Hamilton enjoys a rare feast of line and colour

If you want to kick off a successful exhibition of modern art, reach for Picasso. Relentlessly, irremovably, he has come to define 20th-century art, shaping its images, covering every facet of its artifacts and always projecting his personality.

So it is no surprise that the British Museum starts off its new exhibition of modern drawings in the prints and drawings gallery with a work by Picasso – a rather special one, indeed. It is a study for his groundbreaking Les Demoiselles d'Avignon, of 1907. Or perhaps it is not a study so much as an idea (and a quite sexual one at that), of a woman with her legs open and crossed. The sideways glance of the face is repeated in the final picture, the pose is not. Which makes the drawing more of a work in itself.

Picasso made somewhere between 400 and 500 studies for his revolutionary painting, an indication of just how important the work was at a time when he was in intense competition with Matisse for the role of "great master of modernism". It is also an indication of the degree to which, for Picasso and Matisse, working on paper was a time-hallowed way of working out ideas for major paintings.

"Studies for", or the continuance of tradition, however, is not what this show is about. Its first wonder is that it is here at all. We have grown used to, and in some cases overwhelmed by, the British Museum's holdings of modern prints. Modern French, modern Italian, modern Japanese, modern British especially – we have had them all and we have been entranced by the breadth and freshness of the holdings displayed.

But "modern drawing" is something new. It turns out that the Museum has been collecting 20th- and 21st-century works on paper for 35 years. These are mostly by British artists but the Museum also owns some 2,000 drawings from other countries. A couple of years ago it held an exhibition of drawings by British sculptors, from Henry Moore to Antony Gormley. It covered a very specific area. Sculptors have always sketched out ideas for three-dimensional forms on one-dimensional paper. It has been the concept of the sculpture that has driven their idea, not the sketch.

Any modern exhibition is bound to pose the question of where drawing stands in an art world which, very early in the last century, abandoned conventional drawing and painting for collage, improvisation and, now, installation art.

It would be unfair to demand an answer from this show. The Museum would not claim to have a comprehensive collection of modern drawings. It started too late and it did not have the funds. This show also appears to have been put together fairly quickly, in view of a delay in the next scheduled exhibition. Didactic it is not.

Still, in an odd way, it works. Put together as much on the basis of idiosyncratic taste as thematic logic, Picasso to Julie Mehretu: Modern Drawings from the British Museum Collection displays a wide range and timespan of works on paper, ordered by visual grouping as much as chronology. It includes a welcome assembly of German and northern European artists and a number of names that were entirely new to me.

Picasso was – like Matisse – a great draughtsman. He sets the scene not just with the study for Les Demoiselles d'Avignon but with a marvellously fresh and cheerful Leaping Bulls, drawn and coloured in 1950 as the first page of the visitor's book for the then recently established Institute of Contemporary Arts. In addition there is a drawing of a Nude Girl, from 1903, that is of breathtaking confidence and fluidity.

Matisse's Female Nude of the same period, shown alongside, suffers a little in comparison. Slightly contorted, it is very obviously a work made with Matisse's planned sculptures of the female back in mind. But then the Frenchman comes into his own with a large and magnificent charcoal study, Woman Seated in an Armchair Wearing a Taffeta Dress, from 1938, the body and the serpentine lines giving a monumentality to a full-length figure in a patterned gown.

Matisse wrote: "The emotional interest aroused in me by the models does not appear particularly in the representation of their bodies but often in the lines distributed over the whole paper, which form its complete orchestration, its architecture." That, as so often with Matisse, the quiet radical of art, sets the tone of many of these drawings.

Woman Seated in an Armchair... is shown in a group of works that set out to achieve a finished-work force. This group includes Hans Burkhardt's charcoal of a figure as mechanics and Richard Haizmann's powerful Head, from 1924. On the end wall, by the door, are two tremendous figure studies of more recent date, Jim Dine's charcoal, The Die Maker, from 1975, and an RB Kitaj of three male figures viewed from the side that was made in coloured chalks in 1978.

It is the grouping of the works into three and fours which makes this exhibition an unexpected pleasure. Although the show is being presented as a "survey of modern drawing", "showcasing some of the greatest artists of the 20th and 21st centuries", that is not really its attraction.

Yes, there is a roll call of the big names – not least pre-war German modernists, for which thank heavens, considering the paucity of their paintings in British public collections. There are half a dozen Ernst Ludwig Kirchners, including a vigorous pen and ink and watercolour view of The Artist's Studio and a typical Studio Scene with Three Female Nudes. Both are from before the First World War. The pall of that dreadful conflagration hangs over works that came during or after it – Otto Dix's Woman Giving Birth, a quite devastating and devastated work in brush and pen; a George Grosz cacophony of particular grotesqueness, People in a Café, of 1917; and Max Beckmann's Hogarthian The Street, from 1919. There are also three studies by Beckmann, for Fastnacht.

The symbolists are represented by a very polished La Géante, a graphite picture of a leaf as a tree by René Magritte, and Giorgio De Chirico's Metaphysical Figures, as well as a quite delightful untitled work in pen and black ink from 1947.

If this were an exhibition only of masterpieces, it would be incomplete and stretched, good though some of the drawings are. What we have instead is a wonderfully eclectic and varied selection of works, of varying quality and infinite variety in technique and style. "Drawings" is not quite the right word; the title of the show should have referred to "works on paper". That widens the scope, not just regarding the works, but the materials.

Pencil gives way to charcoal and ink, which soon becomes the medium of choice, being expressive in the work of the Germans but also infinitely adaptable for the abstract pictures of Franz Kline, Charles Seliger and Kazuo Nakamura. Graphite, for the same reason but with more precision, is used to give extra edge.

At the extreme, we have Olav Christopher Jenssen's drawings for Knut Hamsun's 1890 novel, Hunger, in which the paper has been waxed, incised and drawn upon. What the naturalist author would have made of them is another question.

Whether you can make out any firm themes or patterns in these 70 works seems doubtful, other than regarding the variety of techniques. It is a show best taken in not by shuffling round the drawings in order – the normal form for such exhibitions – but by walking through the middle and going to the groupings as they take your fancy. It is a free show, after all, which we the taxpayers are funding.

If this is what the British Museum is up to with its collection purchases, one can only say, "Good on them." Huge expenditure on only the very best works is not realistic, given today's art market and the general climate of cuts. What we have here is a representation of the Museum's holdings which is fun, intriguing and often enlightening about a period when paper, like canvas, was very far from dead.

What one now looks for are bigger, more carefully planned shows on particular themes and schools – not least of modern British work on paper, of which the British Museum has far larger holdings.

Picasso to Julie Mehretu: Modern Drawings from the British Museum Collection, British Museum, London WC1B (www.britishmuseum.org) to 25 April