Today, on the centenary of his birth, Bertolt Brecht's reputation as a dramatist lies in tatters, amid revelations that he may not even have written his own plays. High time then, says Michael Glover, to hail Brecht's true and lasting artistic legacy: his poetry.

Idle serendipitously through WH Auden's commonplace book, A Certain World (first published in 1971), and you will eventually arrive at a section called, in characteristic arsy-versy fashion, "Unfavourites and Favourites", which lists his personal choice among living poets.

First among Auden's "pets", as he called them, was "Berthold Brecht (lyric poet)". To those who think of Brecht primarily as a playwright and a theoretician of theatrical practice, and are scarcely aware of his vast output of poetry outside the songs and lyrics embedded within the plays themselves, this judgement will come as something of a surprise. In fact, the more closely we read Brecht - the 100th anniversary of whose birth falls today - the more it seems that Auden was right in his assessment. Brecht the dramatist will, I suspect, increasingly come to be regarded as second-rate (whether or not he actually wrote most of the plays that bear his name); it is Brecht the poet whose reputation will endure.

Auden knew Brecht when they were both in exile in America during the 1940s. He collaborated with him on a version of The Duchess of Malfi, translated his Caucasian Chalk Circle, and produced versions (some loose enough to be called imitations) of other poems of his (some of them turned up in a late collection called City Without Walls). But the two were never close friends, especially not in later life. In fact, Brecht came increasingly to be demonised by Auden. "He was simply a crook," Auden told Charles Monteith, his editor at Faber & Faber. "He never gave up either his Austrian nationality or his Swiss bank account."

Such vehemence helps to disguise the fact that Auden and Brecht were rather similar in a number of ways. Romantic anarchists in their youth, they both became ideologues - although passionate adherents of opposing ideologies, one secular and Marxist, the other sacred and Christian.

But why are the poems themselves so little known? Brecht himself was partly to blame. In spite of the fact that he was writing poetry from his school days in Augsburg, and consistently throughout his years at Munich University, he always regarded the writing of poetry per se as an essentially private activity, and the publishing of it as relatively unimportant. The theatre always came first. During his own lifetime he published only three small collections of verse, the second and third of which appeared in emigre editions; the Nazis violently disapproved of it; and the overall consequence was that the greater part of his poetry remained unpublished at the time of his death. When the Collected Poems eventually appeared in English translation in 1976, 20 years after Brecht's death, the quantity and quality of his verse astounded new readers.

In his general introduction to the Collected Poems, John Willett, the veteran Brechtian who has been one of the joint editors responsible for the publication of Brecht's complete works in English, and whose Brecht in Context (Methuen, pounds 12.99) has just been re-published to coincide with the centenary of the writer's birth, called Brecht the poet "an unsuspected time bomb ticking away underneath the engine-room of world literature".

The literary influences upon Brecht's poetry are legion, and they are especially visible in the earlier work - there is Villon, Rimbaud, Whitman, Shelley and, above all else, the Lutheran Bible. When he first began to write, he crafted his poems as lyrics for the guitar in the tradition of the Munich playwright Frank Wedekind (author of the Lulu plays and other "sex comedies"), and this matter of verbal presentation would always be of crucial importance to him. In a long and detailed essay on rhymeless verse, published in 1939, Brecht makes this clear: "I was always thinking of actual delivery," he writes.

For Brecht, language, in the words of John Willett, "had to convey the attitude of the speaker and the precise force and weight of the thing said". He was, above all things else, a performance poet, though a weighty one when the occasion demanded. But not always weighty. Brecht's variousness as a poet is astounding - he can be flighty, ironic, savage, grim; he can write forceful narrative poems in the manner of Kipling, whose work he knew, admired and even recycled; he is also, at times, given to the kind of visionary excess at which Rimbaud excelled in Le Bateau Ivre. In later life, his range narrows terribly as Communist ideology begins to gain a stranglehold of his imagination, and his poetry begins to sound wooden and formulaic; but in much of the early work there is a fresh, astonishingly individualised voice at work.

Brecht's first book of poems, Devotions (1927), is both savage and playful. The tone is mock-sacred, the influences range from the Bible to hymns and chorales. Brecht himself, ever eager to annotate his own thought processes in fiercely didactic fashion, produced a series of notes to accompany different groups of poems within the collection, such as the following: "The Third Lesson ('Chronicles') should be consulted in times of crude elemental violence. In times of crude elemental violence (cloudbursts, blizzards, bankruptcies and so on) it will be found helpful to turn to the adventures of daring men and women in foreign parts such as are provided by the 'Chronicles', which are kept on so simple a level as to make them suitable for use in primary schools. At any performance of the 'Chronicles' it is advisable to smoke; the voice may be harmoniously supported by a stringed instrument."

But the issue of privacy is only one reason for the neglect of Brecht's poems. Their publishing history has also been complicated by the difficult times through which he lived, and by his own strident political beliefs. This week, for example, there is published in English translation for the first time a book entitled The War Primer (Libris, pounds 35) which Brecht wrote before and during the Second World War in the various countries where he spent his 16 years' exile - Sweden, Finland and the USA. During the years in America, he was in the habit of annotating pictures from news magazines with his own satirical quatrains. Epigrammatic verse seemed a suitably forceful way of commenting upon images from the mass-circulation press. By the time the book was complete, it contained almost 90 such little poems, complemented by press photographs of scores of grisly or heart-rending scenes.

When, in 1949, Brecht eventually returned to the German Democratic Republic (the former East Germany) and tried to find a publisher for the book, it was deemed to be too pacifist in outlook, too generally censorious of the practice of war, and quite out of touch with the mood of the Cold War years. The view from the West was no more kindly - this was Brecht in full, anti-Capitalist voice, shrill and dangerously radical. A censored edition of the book was eventually published in East Berlin in 1955, a year before Brecht's death, but The War Primer had to wait until 1994 for a full German edition - and until this week for its first appearance in English. Some of the quatrains do not rise much above the technically competent; others are poignant exposures of the meaninglessness of war. They all testify to Brecht's continuing belief that, even in the most difficult of times, verse can pack a punch.

And these photo-epigrams also remind us of poets of our own time upon whom Brecht has had a powerful and enduring influence - that bard of the newspaper and the small screen, Tony Harrison, for example.