Only a few years ago you would have been offered long odds on the British Museum overtaking Blackpool Pleasure Beach and Tate Modern to become Britain's most popular attraction. But then this is just the sort of improbable coup that people have come to expect from Neil MacGregor, the British Museum director and architect of its swelling popularity. MacGregor has measured out his life in unlikely triumphs. Go back two decades, and you would probably have been offered even longer odds on MacGregor being lured away from his job editing The Burlington Magazine, a fine arts monthly, to run the National Gallery - given that he had, until then, never spent a day working in a museum.

Yet deploying the lightly worn scholarship, political guile and social flair that would soon become his trademark, MacGregor handsomely rewarded the faith of the National Gallery's trustees who had hired him as director.

So when the job of running the British Museum fell vacant six years ago, MacGregor was the obvious candidate. Once there, he briskly set about redefining the role and the ambition of what had become a lumbering institution. Today the British Museum can justifiably claim to be perhaps the best museum in the world, a museum that is inventively exploring and flaunting the breadth of its collection. For this, MacGregor deserves much of the applause. Last year the museum drew six million visitors. On one day the crowds queueing to see its Chinese Terracotta Army exhibition grew so long that, for the first time since the Chartist riots of 1848, the museum gates on Great Russell Street had to be shut to prevent more people coming in.

In six brief years, MacGregor has rattled the prejudices of those who dismiss museums as cemeteries of the arts. He has also cemented his status as the museum director's museum director. For these reasons The Times today chooses him as Briton of the Year.

MacGregor has made the revival of the British Museum's fortunes look so gracefully effortless that it is easy to underestimate the challenges he inherited. When he took over as director in 2002, morale was low. Staff were picketing over redundancies. The museum's deficit had bulged to £5 million. But having landed what he has called “the most interesting job in the world”, he began instilling in others the same wonderment for museums that had seduced him on Saturday afternoon visits as a schoolboy in Glasgow. Crowds were infected by MacGregor's passion.

To MacGregor, the British Museum “remains one of the great achievements of the Enlightenment, an enduring statement that the public realm is intellectual and spiritual as well as physical and economic, and excludes nobody.” He believes, moreover, that this “access to information and knowledge, to the greatest achievements of humanity, must be free to all”.

Little surprise, then, that when he was courted this year to take over as the next director of the Metropolitan Museum of Art in New York, MacGregor ruled himself out of the running on the ground that “the Met is not a public museum - whereas the British museum is a public institution and the public museums of London have always been free to everyone”. He takes evident pride in being a public servant. Although he has never discussed his reasons, MacGregor quietly refused a knighthood in 1999.

Neil MacGregor has ensured that the British Museum is not just a venerable but little visited institution, is not just part of an antique cultural landscape, but is vital to the nation's lifeblood. While other museums may wither, MacGregor has made it impossible to imagine a cultural future for Britain that does not feature the British Museum close to its heart. It is a huge legacy.