Theatre and Performance Galleries, Victoria and Albert Museum, London

I have two lifelong addictions - museums and live theatre. There is rarely a week in which I do not indulge in either or both.

I am privileged to have worked in each of these disciplines, but have always worried that the two might be incompatible. Theatre is transient. The butterfly moves on stage. Museums pin the creature to a cork board. It remains a butterfly, but is dead. Can live performance ever be truly represented in a museum or are there some things beyond the skills of curators?

The Victoria and Albert Museum (V&A) opened its Theatre and Performance Galleries in March and clearly believes that it has those skills.

It proclaims its intention "in a fresh way… to show the whole spectrum of live performance". The exhibition is divided into formal sections "focusing on the process of production from initial conception… to opening night".

All genres are represented, from straight and musical theatre to ballet, opera, circus, magic, pantomime, puppetry and popular/rock music. As the curator, Kate Dorney, says: "Everything that happens live in front of an audience is within the remit."

The V&A boasts the most extensive theatrical collections in the world - more than half a million playbills and programmes, 7,500 costumes, 20,000 stage designs, over 20,000 prints and posters, 1,000 prompt books and so on. From this vast treasury it has plucked just 250 artefacts to illustrate the history of live performance in Britain over more than three centuries.

Mixed media

The exhibition starts promisingly and quirkily with the full-size two-man rhinoceros costume from the Royal Court's 2007 production of Eugène Ionesco's Rhinoceros.

Disappointingly, the adjacent video screens were inactive. In the opening glass display case, genres are deliberately mixed. A row of artefacts includes a ballet tutu, the magic piano from Salad Days, a pair of battered Punch and Judy puppets, a rotating, teeth-spinning hook used by a female acrobat and a Gibson guitar smashed on stage by the Who's Pete Townshend.

There are some scattered delights in other cases: a Shakespeare first folio; Sheridan's rewriting of a draft of The School for Scandal; an accounts ledger that shows how audiences plummeted the night that Oscar Wilde was jailed for gross indecency.

The costume section features Richard Burton as Henry V, Laurence Olivier in Oedipus Rex, and Maggie Smith as Lady Bracknell, all side by side with jumpsuits worn by Jimmy Page and Mick Jagger.

These are complemented by an outrageous Dame Edna Everage breakfast frock and two pantomime dame costumes worn by Billy Dainty. Similar juxtapositions are shown in cases devoted to headgear and stage props.

From dead displays…

This display method recalls the old Renaissance cabinets of curiosities, except that these were crammed with objects to instil wonder and amazement. The V&A's cabinets are elegantly underfilled. The influence is less that of historical cabinets of curiosities, more of New Bond Street shop windows. Style rather than substance rules.

Visitors are invited to view a replica of Kylie Minogue's dressing room and are exposed to a display of playbills plus a room full of stage models by Edward Gordon Craig, Alison Chitty, Ralph Koltai, John Piper, Edward Burra and others. Despite the lustre of the names, the effect is deadening. I tfeels like Pompeii.

There is a brief attempt to show some flickers of real performance. Edited clips of a dozen or so productions are projected onto a wall. Unfortunately, the seating area is directly next to the replica Victorian rain and thunder machinery, so that any dialogue is inaudible when these are in use.

The last room, designed for temporary exhibitions, currently features the work of performance photographer Reg Wilson (until 10 January 2010). But it feels like the galleries simply peter out. Is this through a lack of imagination or adequate budget?

Clearly few of the V&A's ambitions are realised. If this were a show, it would close in a week. The intentions are worthy; the results are far from worthwhile. Playwrights remind us the world is a stage; the stage is a world of entertainment. But there is little sense of entertainment or of edification.

"Welcome to the theatre," goes the song, "To the magic and the fun/ Where painted trees and flowers grow/ And laughter rings fortissimo." Well - the painted trees are here in abundance, but there is no laughter, not even pianissimo, and decidedly neither magic nor fun.

I wonder if the problem is the lack of outside imagination. The design and execution is entirely in-house and pedagogic. As Alan Bennett commented in Forty Years On: "This is the school play, you know. You are not here to enjoy yourself." … to live alternatives

So what is to be done? Peter Brook at the end of his seminal book, The Shifting Point, made a whimsical but wise observation: "God, seeing how desperately bored everyone was on the seventh day of creation… saw a further aspect of reality… so he invented theatre."

The V&A has, alas, restored boredom. Vital elements of theatrical life are missing. Where is the counterpoint between performers and audiences? Why no reference to critics? Where is Shaftesbury Avenue glitz and razzamatazz?

Instead the atmosphere is sombre and over reverent. These are not galleries that challenge the visitor, but reliquaries in which a few bits of theatrical detritus have been thrown together.

This space needs activities. Bring in some performers. Fill the cases with more things. Dress the bare walls with more posters and playbills. Market the space more forcefully within the V&A; it is difficult to discover. I had to be guided there. My fellow visitors had found the exhibition by accident.

I am dismayed by the token nature of these galleries. The V&A, controversially but properly, put an end to the shabby displays in Covent Garden in 2007. Now London, the centre of the most potent theatrical tradition since ancient Greece, has no theatre museum.

New York, Vienna, Oslo, Helsinki, St Petersburg, Brisbane, Krakov and most major cities of the world, including Ulaanbaatar, the capital of Mongolia, do. It's about time that someone with passion and pizzazz in the V&A said, "Let's do the show right here!"

Peter Lewis is a writer, a past director of Beamish, and a former marketing director of the Royal Exchange Theatre, Manchester