So successful is the formula - of top author meeting adoring public - that not only do similar events occur in towns across the country, but the literary festival, complete with British authors, has become one of our greatest exports.
From Buenos Aires to Venice, Jerusalem, and Adelaide; across to Melbourne, Mantua and Frankfurt, or Gothenburg, New York and Toronto, British writers can be found at bookfests based on Cheltenham's and Hay-on-Wye's festivals.
"The English language is a phenomenal tool," said Peter Florence, who founded Hay in 1988 and who has just taken up the post of director for what promises to be the mother of all book festivals, the 10-day, pounds 1m- London festival in 1999.
"It's right we should shout about it in every possible way. Language is a common currency and in that sense the literary festival can be seen as a British export," he said.
It was a point endorsed by Dr Harriet Harvey Wood, head of literature at the British Council from 1980 to 1994. "English is an international language and it has given us an unfair advantage," she said. "The British Council promotes Britain abroad and literature is one of the most useful ways of informing people about a country."
Dr Harvey Wood believes there are several reasons why the foreign literary festival, even in non-English speaking locations, such as Sao Paulo or Buenos Aires, has a strong interest in British books and poetry.
"We do happen to have lots of jolly good writers who are in demand abroad. If I were Italian I would rather pick up a British author than a French one. British literature was highly prized in Soviet Eastern Europe. Reading it was a way of making a political statement."
Among those who have turned up at book festivals, as well as book shelves, across the world are Doris Lessing, Ruth Rendell, Malcolm Bradbury and Hanif Kureishi. For an author it is a no-lose situation. The British Council, your publisher or festival organisers will pay your fare and your accommodation; you simply swap ideas with an admiring public, sign and sell copies of your books and meet fellow authors.
There are practical reasons why British writers feature prominently at overseas festivals, according to Mr Florence. "The British publishing industry is very good at getting writers' books out in print in local languages and clear the path for the authors. In countries where English is not the first language you find many authors sell more in English than in their original language," said Mr Florence.
"In many countries, an awareness of English literature and poetry is well established. For many poets it is standard practice to translate the works of people like Byron, Auden and others. I saw 600 people listening to Hanif Kureishi and Salman Rushdie at the Mantua festival in Italy.
"All festivals are very specific and different and the international festivals take on their own character. Toronto is the most cosmopolitan city in the world, even more so than New York. Its harbourfront festival is smaller than some in Britain but it has a specific agenda. Local communities tend to support authors from the same ethnic origin."
Britain, of course, remains sardine-packed with literary festivals: apart from Cheltenham and the other high-profile occasions at Hay-on-Wye and Edinburgh, many of the world's leading writers and poets embark on a year- long circuit of festivals that take in, among others, Birmingham, Brighton, Cardiff, Chester, Cornwall, Bath, Devon, Salisbury, Swansea, Newcastle, Darlington and Norwich.
The turn-over is considerable, in terms of both authors, readers and money. This year's festival at Hay staged 163 events and attracted 33,000 people to the small town, which for the rest of the year is home to just 1,300 inhabitants and an astonishing 30 bookshops, making it the second- hand bookshop of the world.
Brian Perman, of the Book Trust, which promotes literacy in the UK, took a pragmatic view of the trend. "A lot of money is being made from literary festivals. There is a growing demand to meet authors and hear them talking about their work. I suspect getting a signed copy of their work plays a small part, too."