In a glass-walled conference room at a well-known music publishing house overlooking the roofs of London, the 53-year-old British composer Judith Weir, the subject of a mini-festival by the BBC Symphony Orchestra at the Barbican Centre and on Radio 3 this month, is talking about her career. She is a narrator-composer who tells stories through music. Audiences come away not only entertained, but also informed. For this reason, the pending intensive weekend concert series is called "Telling the Tale".

At the climax of the festival, Weir will tell the story of London in her latest work, CONCRETE, commissioned by the BBC Symphony Orchestra. Inspiration came from the area around the Barbican itself, which was the site of ancient Londinium's fort. Strangely, a firebomb raid in 1940 destroyed local housing but exposed for the first time the 1,500-year-old Roman battlements beneath. "This started me thinking how cities rise, fall and rise again," says Weir in her soft Scottish burr, "and how the ancient city is still there beneath the new. It's a story of life perpetuating itself. That is the central idea in the piece."

The capital letters that appear in the title are there "for their slab-like, industrial effect," she explains. "I've become a bit of an enthusiast for concrete. It's immune to fire. You mix the ingredients with water and it turns to stone. The construction is simple, yet the result is strong enough to build to 30 storeys. There's an obvious analogy, too, with musical composition."

Weir is carrying the enormous breeze-block of the manuscript under her arm. She is still in the process of orchestrating it - strings, wind, percussion, voices. Of these sand-and-grit constituents, the dominant element is the choir.

"Knowing that I was going to write one, I have been to loads of chorus and orchestral works over recent years," she says. "My criticism of lots of performances is that the chorus often seems rather in the background. I really wanted this to be about chorus singing. So I am orchestrating it, shall we say, 'motet-style', in that what the chorus sings is always the main focus, with a section of the orchestra provided to help them out, to make their colours brighter."

I ask where she found the texts that the choir sings, and she reels off an eclectic list. The piece does not tell the story chronologically. There is a narrator who, throughout the work, delivers extracts from John Evelyn's "very exciting and incredibly vivid" account of the Great Fire of London in 1666. "I think he must have been wandering around in the ruins," Weir says. There are passages from John Stow's Survey of London, Henry Mayhew's London Labour and the London Poor, a Roman sentry's song from the Penguin Book of Latin Verse, a fragment of the Greek liturgy used in the cult of the bull slayer Mithras, worshipped by pre-Christian Roman Londoners at a temple on Queen Victoria Street, the ruins of which still stand, and Shakespeare's Sonnet 55, which speaks of love outliving the crumbling of cities.

Words and texts are important to the composer, who reads voraciously and widely. As a child, she was surrounded by the case histories of the mentally ill, her father being a psychiatrist at a hospital in Wembley, Middlesex. The family lived in the grounds. Both parents were amateur musicians and she took up the oboe, achieving selection for the National Youth Orchestra.

She went to school at North London Collegiate, which is built on an estate once owned by the Duke of Chandos, Handel's first British employer. Through her music teacher she sent compositions to John Tavener, who took an interest and put her in touch with the Society for the Promotion of New Music. "This was encouragement of a practical sort, which was very valuable at the time, and I shall be forever grateful to him," she says meekly.

Weir was the second female student to enter King's College, Cambridge. She read music, joined the Labour Party and pursued an extracurricular interest in Chinese culture. She now regrets that this was not her degree subject; it has certainly influenced her work, especially her operatic debut, A Night at the Chinese Opera, a film of which is to be shown during the festival, and the Taoist solo cantata Natural History, which opens the Barbican programme. The opera relates a tale from the time of Marco Polo and uses the orchestra like a traditional Chinese band. The cantata takes four ancient anecdotes about human and animal life and connects them to the present.

In both these works, the stories are classics, but the actual words are Weir's own. Her re writes are pithy, spare and concise, and give shape to the music, which shares these traits. The same characteristics, in fact, apply to all her scores. The music is never verbose, long-winded or stuffy. It is intriguingly melodic, vividly atmospheric and often crisply witty. Listeners cannot miss the humour of King Harald's Saga, in which a solo soprano represents all parts, including the entire Norwegian army, or The Art of Touching the Keyboard, in which the pianist must also be a contortionist. Both pieces appear in the festival.

She describes Taoism as the most helpful of all the established philosophies in the conduct of modern life. "It encourages you to take things easy in an active way. I have long been interested in Zen ideas of losing everything and going for the moment. Music has a lot to do with this and I've found it helpful in composing. I have a mental image of throwing everything away and starting afresh each time."

The interest in Chinese philosophy was sparked by her fascination as a teenager with the composer John Cage, perhaps the most influential thinker about music of the 20th century. She later met Cage through teaching work at Glasgow University, and there is the unmistakable imprint of Cage's clarity, charm and perception in all 30 of her works programmed for "Telling the Tale" - the operas (the Scottish folk tale-inspired Vanishing Bridegroom is to be staged); the orchestral music, as in CONCRETE; the chamber music, such as the Piano Quartet; and the short engaging songs. There is wisdom in all of them.

"Cage encourages you to take a step back," Weir says as we look out over the rooftops. The sounds of the city are faint through the glass. "His thing of listening, using your ears - you can't be reminded of that enough, really."

"Judith Weir: Telling the Tale" is at the Barbican, London EC2, from 18-20 January. The concerts will be broadcast, sometimes live, on BBC Radio 3. Visit: www.barbican.org.uk and www.bbc.co.uk

Judith Weir

1954 Born 11 May in Cambridge

1972 Studies with the composer John Tavener while still at school in London. Later, at King's College, Cambridge, she is tutored by Robin Holloway. She then spends several years as a community musician in rural southern England

1979 Produces her first major work, King Harald's Saga, an opera in three acts that runs for just ten minutes

1987 Premiere of her first full-length opera, A Night at the Chinese Opera. This is followed by The Vanishing Bridegroom (1990) and Blond Eckbert (1994)

1994 Receives a Critics' Circle Music Section Award for her outstanding contribution to British musical life

2000 First performance of the chorale We Are Shadows, which uses over 300 performers

2004 Fromm Foundation visiting professor of music at Harvard University

2005 Broadcast of her television opera Armida, controversial for its allusions to the Iraq War

2007 Becomes the third recipient of the Queen's Medal for Music

Ben du Preez