When the 78-year-old widow of a Swiss baron last year found herself locked in negotiations with the Spanish government over how much it would pay to rent her late husband’s art collection, she had a brainwave.

Unsatisfied with the offer from Madrid, Carmen Cervera, a former Miss Spain who was married to Baron Hans-Heinrich Thyssen-Bornemisza, simply removed a much-loved painting by Paul Gauguin she owns from the museum walls.

Mata Mua was sent to her private vault in Andorra, denying the Spanish public the chance to admire the lush Polynesian landscape, considered a particularly valuable piece.

On Wednesday, Madrid appeared to cave in to her demands, agreeing to pay her €100m to rent the whole collection – on the condition that she return Mata Mua to Spain within 72 hours.

Critics have also argued that the collection has been overvalued, and questioned whether it’s worth the large slice of public money.

Mata Mua is a lush Polynesian landscape painted from Gauguin’s imagination in 1892, the year after the French artist moved to Tahiti saying: "I’m off to live with the savages".

Mata Mua (In Olden Times), 1892, by Paul Gauguin

Credit: Hulton Fine Art Collection

Ms Cervera, the fifth wife of Tarzan of the Apes film actor Lex Barker, has also removed paintings by Edgar Degas and Edward Hopper from her collection, which includes 425 works of art.

The agreement, passed by Spain’s Cabinet and which is expected to be signed in coming days, sees the dowager baroness receive €6.5 million annually for lending her collection to the Spanish state for a guaranteed 15 years.

Ms Cervera is reported to have sold one of Claude Monet’s series of paintings of Charing Cross Bridge, although she denies that one such cityscape that appeared in the Louvre Abu Dhabi at the end of last year is hers.

“I have complete freedom to sell whatever I want,” she said in an interview in May, adding that the loan deal, once signed, would allow her to retain total control over two works from the collection, but Mata Mua would not be one of them.

In 2012 Ms Cervera stunned the Spanish art world by withdrawing John Constable’s The Lock from the museum and auctioning it for £22.4 million at Christie’s in London.

“I have lost a fortune by collecting for Spanish museums,” Ms Cervera, who has also founded a museum in Málaga, told the ABC.

While the million or so art lovers who visit the Thyssen-Bornemisza each year will breathe a sigh of relief that the rich hues of Gauguin’s Mata Mua will remain on display at the museum, art experts have questioned the size of the deal and whether the baroness’s collection is really worth such a large public spend.

Some critics claim that the Spanish Culture Ministry has negotiated the agreement without commissioning a report to ascertain the true value of the works.

“When the state pays for a collection, the operation is always backed up by technical report by experts, who consider its worth,” Isabel Tejeda, a professor of art history at Murcia University, told the online newspaper El Diario.

“This collection is not excellent; it lacks a strong focus,” Prof. Tejeda added.

Ms Cervera claims she has turned down an offer of €250 million for Mata Mua and that her collection is worth €1.3 billion, but the Spanish state’s insurance policy for the artworks is reported to be less than €400 million.

The Baron, Baroness and daughter photographed together

Credit: Rex Features

In 1981, as a twice-divorced single mother and with her acting career faltering as Spain lost its appetite for the frivolous comedies of the 1970s, Ms Cervera met Baron Thyssen-Bornemisza when a cruise she was on stopped in Sardinia.

They married in 1985 but he died at the age of 81 in 2002.

The baron’s art collection, which at one point had 1,600 paintings, was believed to have been the second largest in the world after the British Royal Collection, and in the 1980s he decided to seek a city home for it after being refused permission to enlarge his own museum in his Lugano mansion.