I'm sitting on the floor with a piece of cardboard attached to my head by one of those rubber bands that postmen drop; across the room by the window, my three-year-old grandson Thomas shouts “Masks On!” and pulls his bit of cardboard lower over his face. I do the same.

My wife comes in and looks quizzical. “We're firefighters,” Thomas explains, “and there's a fire at the shop and we need sirens and masks because there's smoke” - and then he's straight into his impression of a siren and we're putting out the fire with drinking straws.

It might seem a bit of a leap from my front room and a couple of cardboard masks to the Pit at the Barbican Centre in London and a performance storytelling series called The Matter of Britain this coming week, but it isn't, because as little Thomas knows, the urge to make and to listen to stories is deep within us all, pouring out in playground games, pub anecdotes and fishermen pulling their arms wider to exaggerate their catch. For years the Barbican has hosted events and workshops curated by that most vital and exciting storytelling organisation, the Crick Crack Club, and The Matter of Britain is one of a series of seasons proving that storytelling is alive and well.

The thing about storytelling is that it is not the static artform that people often think; it adapts and changes because stories have always adapted and changed; this series includes a new show by the teller Hugh Lupton and the award-winning musician Chris Wood, about the enclosure acts, as seen by John Clare, one of the greatest visionary nature poets that England has produced; Katy Cawkwell's Welsh tales, including versions of the Mabinogion, and Ben Haggarty and Sianed Jones's epic tale Midir and Etain, a love story that spans 1,000 years.

These are all master (and mistress!) storytellers, used to holding a room thrilled and attentive simply with the power of narrative and language; I once saw Haggarty, fresh from a long and bumpy plane ride, captivate a huge restaurant full of diners in Buenos Aires. We had just eaten something that looked suspiciously like the penis of the vaquero's favourite bull (maybe I'm exaggerating, but that's part of the storyteller's art) and it didn't seem that much could top it: Ben did, transporting us to magical places as the waiters collected plates and the traffic roared outside.

Thanks in many ways to The Crick Crack Club, of which Ben and Hugh are founder members, storytelling is on the crest of a wave at the moment, and not just at the Barbican. You can visit festivals such as the Festival at the Edge, which takes place every July in Wenlock Edge, Shropshire.

If you are in Edinburgh you can go to the Scottish Storytelling Centre on the Royal Mile for a cup of tea and a story, and there are storytelling clubs all over the place, from the Shaggy Dog Storytellers in Hebden Bridge to A Bit Crack in Newcastle, Taffy Thomas's Storyteller's Garden in Grasmere, the Brighton Storytellers, and Bristol Stories, a “creative digital storytelling project”.

At its most basic level, the story is the voice and the listener; or the voice and the gesture and the listener; or the voice and the gesture and the prop and the costume and the listener. Another colour on the palette of storytelling, of course, is the interplay between story and music; Lupton and Haggarty are working with musicians at the Barbican, and so am I - with the modestly named Ian McMillan Orchestra.

I have always been interested in the relationship between words and music, in how they can complement and illustrate each other, and the orchestra has been a chance for me to connect with the fundamentals of telling a tale: rhythm, repetition and, above all, improvisation.

So as part of the Sharp Stories show with the orchestra, mixed in with pieces about a quarry in Derbyshire and a trip to Russia, where I sweated my way across thousands of miles in a bouncing car, I make up a story on the spot in response to a suggestion from the audience; it sounds scary but it really isn't. I just pretend that I'm back in our front room with a bit of cardboard on the front of my head. It usually works!

The Barbican's 15th performance storytelling series: The Matter of Britain is on Tuesday, Thursday and Friday at 7.30; The Ian McMillan Orchestra: Sharp Stories is on Wednesday, at the Barbican Centre, 2 Silk St, London EC2, 020-7638 4141, www.barbican.org.uk

Chris Wood's album Trespasser is released this month by RUF Records

Times Recommends

• The 100 Best Books of the Decade
• The Times picks the 50 best paperbacks of 2009
• The conversation: James Ellroy