Searching for Shakespeare, National Portrait Gallery, London

'An illustrious conjecturability' is the delicious phrase coined by Mark Twain to describe William Shakespeare. He was one of 'the best known unknown persons that have ever drawn breath', Twain insisted.

Lustre and conjecture are still very much alive in Trafalgar Square where, as part of its 150th birthday celebrations, the National Portrait Gallery (NPG) has mounted a major exhibition called Searching for Shakespeare.

The show aims to examine evidence about the life of Shakespeare and claims to cast 'new light on the search for his authentic appearance'. Much energy, scholarship and sponsorship money has been spent on a compact display of the few artefacts that seem to relate to the man from Stratford-upon-Avon.

First folios, marriage bonds, account books, theatre plans, costumes and that infamous 'second-best bed' are here. Around the walls are portraits of his contemporaries and patrons - Marlowe, Jonson and Fletcher, Drayton, Donne and Burbage jostle for attention with The Virgin Queen, James I, the Earls of Southampton, Pembroke, Oxford, Essex and others. The result is a fascinating cabinet of curiosities, a relic-strewn temple of bardolatry.

On the rear wall are six portraits, each of which has over the centuries laid claim to represent Shakespeare. Four of these 'contenders' are palpably fakes or portraits of other men. The frontispiece of the First Folio is here, that peculiar engraving in which the head appears to have been superimposed on to the ruff and subsequently on the torso.

And then there is the so-called Chandos portrait, the first picture to be donated to the NPG in 1856, the 'onlie begetter' of the collections, and the raison d'etre for this exhibition. The portrait shows a gloomy Levantine-looking man with a high-domed forehead, a prominent nose and a louche gold earring. It looks a bit like the funeral bust and the engraving, both of which were attested by family and friends as reasonable likenesses.

Scientific testing suggests that the panel and the pigments are of the right age. It is likely the man is a poet. Like an adjacent portrait, assumed to be of John Donne, the sitter is framed in an oval with his collar unlaced, the conventional indicators of an artistic nature. Could this be 'the lunatic, the lover and the poet…all compact…in a fine frenzy rolling'? After all the research, the answer we get is a more assured perhaps.

At a crowded press view for this exhibition, the space was full of flashing lights, scribbling notebooks and urgent interviews to camera, a scene that Shakespeare might have presaged in the Rape of Lucrece as 'a press of gaping faces'. There was more than a whiff of the Da Vinci Code about the occasion, a sense that among the assembled artefacts and images there was a truth waiting to be discovered.

This frenzy was in part fed by the gallery's own press releases in which the admirable Sandy Nairne, the director of the NPG, commenting on the search for 'a definitive image of the writer', referred to the 'holy grail question of whether a painted portrait can ever be authenticated'.

For literary purists such as me, words are paramount. The text should enter the intellect and imagination of the reader unaided and unencumbered by biographical or physiological details. It may be old-fashioned critical theory but I believe it really does not matter what Shakespeare looked like.

It is true that his work abounds with a myriad of metaphors that draw on sight and appearance. But there is always a dichotomy between inner reality and the look of things. Macbeth's observation that 'there's no art to find the mind's construction in the face' might serve well as the motto for this show.

That said, the exhibition is an admirable one, with pictures, papers and artefacts, gathered from galleries, libraries and museums across the world, many of which have never before been on public display; for students of late 16th- and early 17th-century England it is a valuable experience.

The exhibition is well supported by a series of events and lectures, from Peter Ackroyd and Bill Bryson, via Mark Rylance and Michael Wood, to professors Stanley Wells and James Shapiro.

But still Shakespeare is conspicuous by his partial absence. The two ends of his life, the Stratford glover's son and the retired well-to-do gentleman are well covered. But there is no sense of the creative poet and playwright. It is all a touch too scholarly. Despite the best attempts of academics to wrap his work in difficulties, he remains astonishingly accessible and robust.

In the poems of early 20th-century writer Don Marquis, his alter-ego, the cockroach Archy, catches the essence of Shakespeare: 'coarse jocosity catches the crowd… Shakespeare and I are often low browed… aesthetic excuses in bill's behalf are adduced to refine big bill's coarse laugh… but bill he would chuckle to hear such guff… he pulled rough stuff.'

Peter Lewis has worked in the professional theatre and is a past director of Beamish, the North of England Open Air Museum

Project data

Sponsor: Credit Suisse

Curator: Tarnya Cooper

Exhibition design: Charles Marsden-Smedley

Contractor: DHA

Graphics: Impress Print

Lighting: Universal Fibre Optics

Exhibition ends: 29 May