Industries such as music, publishing, fashion design and the performing arts now generate pounds 60bn of revenue a year and employ 1.4 million people.
The first big study of the importance of creative industries to the British economy said the sector had the potential to create 50,000 jobs over the next three years.
The report was issued by the Government's Creative Industries Task Force, whose members include Lord Puttnam, Alan McGee, founder of Creation Records, and the fashion designer Paul Smith.
Chris Smith, Secretary of State for Culture, said the report demonstrated where many of Britain's strength lay. He wanted to avoid a common syndrome in the history of British creative talent: "Invented here and commercially exploited somewhere else.
"The creative industries are not a fringe benefit for Britain's economy, they are right at the heart of it. We are one of the most creative nations on Earth," he said. "With a growth rate of 5 per cent, the creative industries are generating new jobs and new wealth for Britain faster than any other part of the economy.
"Our share of international exports in this sector, at just over 16 per cent, is three times greater than our share of world trade overall."
He said the Government wanted to stimulate further growth by promoting exports, which already generate an estimated pounds 7.5bn a year. Schools will be asked to encourage innovation in young people and action will be taken to protect intellectual property rights and combat piracy. The report also called for new laws to encourage people to set up creative businesses. The creative industries cover areas that are of increasing significance in the global economy, including communications, leisure and entertainment.
British talent is behind two out of every five commercially successful computer games in the world. British publishing firms are worth pounds 16.3bn, design pounds 12bn and television and radio pounds 6.4bn.
The performing arts sector relies on a mixture of public and private finance and the report said that both would benefit from an additional pounds 125m in the arts over the next three years, which would be used to support new productions and increase access.
The Design Council gave a qualified welcome to the report but warned that creativity should not be confined to the film and music industries. Andrew Summers, the chief executive, said: "No matter what sector they operate in, all firms need to be creative and innovative in order to survive."