London's Theatre Museum is to close in January after 20 years because of a lack of funds.
Sir Laurence Olivier's costumes are housed at the Theatre Museum
The museum's future became uncertain when the Heritage Lottery Fund twice refused to back refurbishment plans.
Its owners, the Victoria and Albert Museum, had been trying to formulate a rescue plan with the Royal Opera House.
But Opera House chief Tony Hall said that despite a "huge amount of moral support" for the museum, "money for the most part has not been forthcoming".
Among the exhibits at the museum, which is next door to the opera house in Covent Garden, are Sir Laurence Olivier's costume from Richard III and Noel Coward's make-up box.
The Victoria and Albert Museum (V&A) said it would re-house the theatrical collection in a new gallery on its main site.
Other items will be seen on touring displays, education activities and special exhibitions.
"We remain totally committed to safeguarding and displaying these collections which celebrate Britain's unique theatrical heritage," said V&A director Mark Jones.
The museum has many famous supporters, including actors Dame Judi Dench, Vanessa Redgrave and Peter Bowles.
In March, they wrote a letter to the Times newspaper protesting at plans to close the museum.
"We are horrified that this important and world-renowned museum could be closed and its collection broken up," they said.
They called for "adequate funding" to develop the museum's current site in the heart of theatreland, and "make even more of its outstanding collections available".
Actors' union Equity, which has led a campaign to save the museum, told BBC News: "We are astonished that the world's centre of theatre appears to be unwilling or unable to sustain a theatre museum."
"Our member Vanessa Redgrave has called for the government to step in and halt the closure plans, and we echo that call," a spokesman added.
But Mr Hall said it had become clear the cost of refurbishing the museum is "much higher than originally thought".
The V&A said its trustees would review the situation before their decision becomes final, but added that the museum would be likely to close in January 2007.