The Art Fund Museum of the Year award, worth £100,000 to its winner, is Britain's biggest art prize. As one of this year's judges, Sarah Crompton was overwhelmed by the range and variety of museums she saw.

‘What, exactly, is the definition of a museum?” I asked Bettany Hughes, as we slouched in the back of a minibus during a four-hour journey from London to South Wales.

It’s always handy to have a classical historian travelling with you when this kind of question pops into your head. But really I should have asked earlier. By this point, Bettany and I were more than halfway through our quest to find the Art Fund Museum of the Year, in order to award it Britain’s biggest art prize – a substantial £100,000.

The answer, according to Bettany, is to do with inspiration. The Museums Association expands on that theme, saying that museums (and galleries) are places that enable people to explore collections for inspiration, learning and enjoyment.

Yet those words cannot possibly encapsulate the rich variety I have discovered in the past few months. In that time, the judges – who also include the artist Bob and Roberta Smith, the MP Tristram Hunt and Art Fund director Stephen Deuchar – have agonisingly whittled 40 applications down to a shortlist of 10.

Our finalists covered the country, from Kelvingrove in Glasgow to Narbeth in Pembrokeshire, from Preston Park in Stockton-on-Tees to the Museum of Archaeology and Anthropology in Cambridge, from the Hepworth Wakefield to the Beaney House of Art & Knowledge in Canterbury, from the Baltic in Gateshead to the William Morris Gallery in Walthamstow, north-east London.

The geographical spread seemed thrilling when we were rifling through application statements in the Art Fund’s Kensington offices. When it came to meeting on a rainy morning at some London terminus, ready for a long trip on an overcrowded train, it felt rather less glamorous. I was glad that two of our choices were – totally by chance – more or less a stone’s throw from my home: the Dulwich Picture Gallery and the Horniman Museum in south-east London.

On the other hand, our glorified school trips around the nation have been a revelation. In every case, the warmth of the welcome we have received and everything we have been shown has been both humbling and thought-provoking. My hand has positively ached for the number of times it has been enthusiastically shaken; my head has spun with impressive visitor figures, education plans and collection strategies.

Before I started on this adventure, I had thought – in vague, general terms – that museums and galleries were A Good Thing, that they gave great pleasure and could be a stimulus to learning. What I had not really reckoned with was the kind of pride they engender.

In Stockton-on-Tees, for example, a local authority has taken a rambling, difficult-to-run house, with a sprawling collection of no particular financial value but great interest, and turned it into a showcase. With its own Victorian street, working forge and restored kitchen garden, Preston Park is as full of sparky interest as the friction match invented in Stockton in 1826 – and on display here.
In Narbeth, volunteers not only fought to save their museum when its original site was repossessed, but lovingly filled their new building by donating exhibits that told the history of a small Welsh market town. The most unusual item on display is the Orchestron, a prototype organ; the most touching is a bicycle on which a lovelorn Methodist cycled from Birmingham to court his girl.

This desire to tell the story of people and places is driven not just by a sense of history, but by a belief in the social worth of museums and galleries. Kelvingrove’s aim to offer something for everyone was touchingly revealed by a building so packed with people it was almost impossible to get close to the enticingly child-friendly displays.

But civic pride and a sense of welcome did not exclude scholarship or indicate a desire to head for the lowest common denominator. In Walthamstow, the Labour council leader admitted that in the past his predecessors had not known what to do with the grand house in which the artist, socialist and crafts pioneer William Morris once lived.

But, he declared, he hadn’t run for office in order to close things down – and the result is a magnificently restored building, which explains Morris’s life, work and significance in an eminently approachable way, without sacrificing intelligence or curatorial investigation.

The same is true at the Dulwich Picture Gallery (where I am a trustee and have consequently had to be uncharacteristically silent during all discussions of its application). John Soane’s graceful building embraces not only an extraordinary old masters collection but also a pioneering and distinctive education programme, which has reached out to help the elderly and those with Alzheimer’s. At the Baltic, there is both a rigorous exhibitions programme – which introduced me to the exhilarating work of the French artist Fabrice Hyber – and a learning policy that embraces every school in the area, introducing them not only to contemporary art, but also to its use as as means of communication.

At the Hepworth Wakefield, David Chipperfield’s austere building is enlivened by a curatorial vision that seeks to inspire youngsters – girls in particular – with the story of a Wakefield woman who found international fame. The room devoted to works from Barbara Hepworth’s studio was one of the loveliest we saw.

But the difficulties of using art as a force for social regeneration and motivation were also brought into sharp focus by our visit: the planned restoration of the entire Hepworth Wakefield site, for example, due to be accomplished with the help of private developers, has hit difficulties. In a city struggling with the effects of recession, private companies are not sure they want to restore old buildings for office space.

In such a climate – where cuts to arts budgets are not just a threat but a known prospect – it is impossible not to admire the local authorities who are putting their faith in museums and galleries as assets to their communities rather than a drain on their resources.

Nowhere was this more obvious than at the Beaney House of Art & Knowledge in Canterbury, built in 1899 thanks to the munificence of a dodgy-sounding surgeon known as Diamond Jim, and entirely transformed with the help of a grant from the Heritage Lottery Fund into a place that one local man told us “is the best thing that has happened to this town for years”.

Encompassing a library and the local register office, it felt like a museum that belonged to its visitors, who, on the day we were there, seemed riveted both by Thomas Sidney Cooper’s deeply odd paintings of bulls and cows and by a display of craftsmanship by local jewellers.

This same sense of ownership affects the Horniman in south London. It was founded in 1901 by Frederick Horniman, a wealthy tea trader; now it has been developed to make both the museum and its gardens a place of easy learning and scholarship.

Watching people walk from the old galleries, where a traditional display of stuffed animals is still in place, into the more modern areas is to see the entire history of museum visiting in one place. A similar experience is on offer at the Cambridge Museum of Archaeology and Anthropology, where visitors are being asked how they would like new galleries to be structured – an anthropological study in its own right.

As we travelled around, I started to give each museum a prize. It was Cambridge that held my favourite object, an oar from the boat in which the Maori tribesman rowed to greet Captain Cook. Dulwich had my favourite picture, a delicate Poussin. At Preston Park, I learnt to make wild garlic soup, so that gets my best recipe award, and the William Morris Gallery would win best loos, for the doors were covered in William Morris fabric. At the Horniman, I had my best moment when I held a tiny blue frog, part of an endangered species bred in its aquarium.

But whoever wins the grand prize – and the Clore Award for Learning, worth £10,000 – the lesson I have drawn from my journey as a judge is that Britain should be proud of its museums and galleries. They are run with care, affection and thought – and they really do inspire and enrich the people who use them.

© Daily Telegraph