The Tussauds group, which runs the sites, was put up for sale by Pearson, the media group whose interests range from the Financial Times to Baywatch.
Pearson said it had decided to put the group up for sale after receiving a number of offers for the group. Marjorie Scardino, Pearson's chief executive, said: "We have decided that this is a good time to test whether Tussauds might be even more valuable to a new owner. They will have to offer a good price to convince us that it is." Analysts said the business could fetch more than pounds 300m.
Pearson took over Madame Tussaud's in 1978. Despite competition from other London venues, the prospect of seeing film stars, politicians and leading sportsmen and women recreated in wax has continued to pull in visitors from all over the world. Last year, Madame Tussaud's was London's top tourist attraction, with 2.8 million visitors.
Apart from the London branch, there is a smaller version of the waxworks in Amsterdam and Tussauds is also planning to open new outlets in New York and Las Vegas.
Alton Towers, in Staffordshire, which Pearson bought in 1990, recently launched Oblivion, the world's first vertical roller coaster. Visitors to the park can also enjoy an ice show that features Beatrix Potter's Peter Rabbit.
Tussauds also runs the London Planetarium, which is next door to Madame Tussaud's on Marylebone Road, and the Rock Circus complex in Piccadilly. Other theme parks include Chessington World of Adventures, and Warwick Castle, a historical museum that hosts medieval battles.
Earlier this month, Tussauds agreed to buy the Thorpe Park complex in Surrey, and just yesterday it sold its 40 per cent shareholding in the Port Aventura theme park outside Barcelona for pounds 58m. All in all, the Tussauds venues attracted 12.9 million visitors last year and made a profit of pounds 22.3m.
Analysts reckon the group could attract a number of high-profile buyers. Time Warner, the US media giant, might be interested, as might Universal, the Hollywood cinema group.
In Britain, First Leisure, the nightclub and wine bar operator that also owns Blackpool Tower, may be interested. Rank, the Hard Rock Cafe owner and bingo operator, is also understood to have had a close look at the business.
But industry observers say the Tussauds management team is most likely to win the auction, with the support of a team of venture capitalists.
It may seem puzzling that Pearson wants to sell such a successful business. But the group has recently decided that it wants to concentrate on its media assets, which include financial and educational publishing as well as television. Since Ms Scardino took the helm 18 months ago she has sold off the group's ailing computer games business and its consumer publishing arm. Pearson's stake in the Lazard investment banking group is likely to be the next to go.
1. Some 2,400lbs of wax has been used in the 365 figures.
2. Sculptors require more than 150 measurements of a subject's face and head to create a life-like portrait.
3. About 500 million people have visited the attraction.
4. It takes six months and costs about pounds 20,000 to make a figure.
5. The building survived a fire in 1925, an earthquake in 1931 and some of the worst bombing of the Blitz in 1940.
6. Only real human hair is used on figures.
7. Joanna Lumley is the most touched waxwork.
8. The most photographed figures are those of Diana, Princess of Wales, and Arnold Schwarzenegger.