There's a story that Hans Christian Andersen, a fearful man who thought an accident might occur at any moment, always carried a rope around with him on his travels. The purpose of this rope was that, in the event of a fire, Andersen could throw it out of the hotel window and scramble to safety.

This rope is now displayed in the basement of the Hans Christian Andersen Museum in Odense, Denmark, the legendary author's place of birth.

But is this story about the rope true, or just a yarn? This was much debated by those involved in the Hans Christian Andersen exhibition, celebrating the author's bicentenary, which opened at the British Library in May.

Designer Andrew Lock of children's theatre company theatre-rites, which created the exhibition and associated live performances, wanted to include a replica of the Odense rope. But given the question mark over the tale's veracity, the library was not so enthusiastic.

Even if the story were true, how long was the rope? How thick? The library felt these facts would have to be established to avoid any inaccuracies in its representation. Faced with such uncertainties, it was unclear if the rope would make it into the exhibition.

This rope is a symbol of the tensions between academic excellence, based on a world-renowned collection of books, and accessibility, with which the British Library is struggling.

'When people think of the British Library, they think of the big items. They know the Gutenberg Bible, the Magna Carta, Jane Austen,' says Kristian Jensen, the head of early printed collections. 'This is the first time we've focused on colourful 19th-century books. It's an experiment for us.'

The experiment consists of the library's first exhibition aimed at families and including hands-on interactives.

Theatre-rites was brought on board after Bridget McKenzie, the library's head of learning, visited the Finders Keepers performance and exhibition (both designed by theatre-rites) at the Livesey Museum in south-east London. She was so impressed that she set about convincing the British Library to employ the com-pany for Hans Christian Andersen.

On a relatively small budget of £130,000, theatre-rites took a space in which only cabinets had been displayed before and constructed a giant paper swan, which hangs from the ceiling and is the first thing visitors see.

The interactives are extremely low-tech; there are no computer screens. Instead, simple puppets have been constructed from wood and paper. The Little Mermaid's tail wiggles when you pull the string; the Snow Queen rises from the floor. Cut-outs, based on Andersen's own patterns, make shadow puppets for visitors to play with.

There is an impressive programme of workshops and theatre-rites performances during the school summer holidays. The shows are held inside the exhibition and when there's no performance, there's just an empty space. But the majority of the exhibition is still glass cabinets, filled with books.

I'm a frequent visitor to the British Library, but I've never seen a child there who wasn't in school uniform and accompanied by a teacher. Yet in many ways, and especially the material environment, the library meets the criteria for a child-friendly venue.

There's a large outside space, away from the traffic, and inside is spacious and clutter-free. There are all sorts of items to interest a curious child, from computer screens to temporary exhibitions.

The Hans Christian Andersen exhibition is the library's first attempt to realise this family-friendly potential. But how successful has it been? Part of the challenge is that old books are difficult to display appealingly to almost any age, and books are what the British Library's collection largely consists of; at the Andersen exhibition there are almost 200.

But items such as the first Danish illustrated edition of the Ugly Duckling will only excite a few enthusiasts. Lois Keith, the author of Take Up Thy Bed and Walk: Death, Disability and Cure in Classic Fiction for Girls, says of the exhibition: 'One of the problems of having books behind glass is that you can't do with them what you're supposed to do - turn their pages.'

Sarah Lawrance, the collections manager at Seven Stories in Newcastle, the Centre for Children's Books, which will open this month, acknowledges that books are not good exhibition material on their own.

'Our exhibitions aren't just books in cases. They're about valuing the creative process in making the books. They include preparatory drawings, rough books - all the steps to show how an author or illustrator has moved from the original idea. A book has to be put in a context. If you don't have the materials for that context, you have to create your own.'

Lawrance also says that it is important to have books you can touch and read as well as those you can't; when Seven Stories opens, it will have a Book Den. The Hans Christian Andersen exhibition has a small reading area with a few modern copies of Andersen's work for visitors to flick through, but otherwise all books are firmly locked away.

The books occasionally share their glass cabinets with a toy or related object, such as a rather tired Snow Queen costume. A plastic Buzz Lightyear stands forlornly punching the air in a glass case - an example of an inanimate object that can come to life, as does Andersen's Tin Soldier.

But there is nothing to help the visitor of any age guess why he's standing there so alone and labelled up, and particularly not young children, who are used to seeing the same object lying unceremoniously on their bedroom floor.

Alison Bailey, who is responsible for the library's children's literature, defends the lack of interpretation. 'That's what we're about. We want children to ask: "Why is that there?"' she says.

Although an extra security guard has been taken on for the duration of the exhibition (is this because more potential child visitors mean more potential damage?), there are no enablers to help in this process of discovery. Visitors have to rely entirely on the scarce text panels and a few stationary headphone commentaries.

This paucity of interpretation may also result from a lingering ambivalence within the British Library about the audiences it wants to attract and satisfy.

'It's a fact that a lot of our visitors are adults who are used to very serious academic subjects,' says Elizabeth James, the curator of the 19th-century collection. 'We have to cater to them, too.'

Although some of the visitors to the current exhibition have complained there aren't enough interactives, apparently just as many others have complained there are too many. Andersen's work presented the library with an excellent opportunity to bridge this gulf between different audiences.

His complex, often bleak and demanding writing appeals to adults and children. The words 'told for children' were deliberately omitted from the title when the fairy tales were first published. 'He was rather upset that he was typecast as a writer for children,' Kristian Jensen at the British Library says. 'He wanted to be seen as a fully rounded author, like Dickens.'

Jensen points out that: 'It's not an exhibition for children alone. But we try to make it something that children and grown-ups can have a conversation about. It's new for us.'

This conversational aspect is not immediately apparent; the two different experiences - the interactive and the academic - seem to co-habit the space rather than connect in it. The most accurate way to describe Hans Christian Andersen would be an exhibition for committed adults with add-ons for kids.

Often it is as if there are two exhibitions sharing the same space - the old books in their glass cases and the simple interactive models on the exhibition floor.

Theatre-rites' Andrew Lock hoped to be able to more effectively bring the ideas suggested by objects in the cabinets out to the hands-on experiences, describing his work as 'the pages of the book being freed from its binding'. Still, he admits that the links between the two are weak, reflecting, he said, tensions between 'the academic and the fun'.

So does the British Library intend to keep on tackling this tension, or is the Andersen exhibition a one-off experiment? Its next exhibition, opening in December, Beautiful Minds: Celebrating the Nobel Prizes, is unashamedly academic.

But next spring it is putting on Hold the Front Page, the working title for an exhibition celebrating the centenary of the Newspaper Publishers Association, which will draw on the library's newspaper archive at Colindale.

Hold the Front Page intends to be 'education focused and for families'. It will include a new level of visitor involvement for the library, with an interactive newsroom where visitors can create their own front page on a computer screen, print it out, and take it home.

And as for the rope? Well it may not really have existed at all, but there the replica of it hangs, in the section of the exhibition dedicated to Andersen's life. Lock would have liked visitors to have been able to hold it, but it is attached firmly to the display and not to be touched.

Still, Lock says: 'This is not the Science Museum. This is the British Library. It's a starting point.'

Dea Birkett is the founder of the Kids in Museums Campaign, www.deabirkett.com