There were no Guggenheim fellowships or MacArthur awards for the jazz musicians of the immediate post-war era, a time when their idiom was arguably at its most vital and inventive. What they, or at least some of them, had was the Baroness Nica de Koenigswarter, among the most extraordinary and unorthodox patrons of 20th-century culture.

Born in 1913, the former Kathleen Annie Pannonica Rothschild spent her early life in a manner that passed for normal among the girls of her family  brought up in grand English country houses, educated by governesses, presented at court, barred by her gender from working in the family bank, then betrothed to a French nobleman  until a simmering attraction to jazz, already ignited before the war, turned into a blazing affair that would consume the rest of her life.

By her own account it was hearing a record by Thelonious Monk that inspired her to leave her husband, Baron Jules de Koenigswarter, an aviator and diplomat with whom she had served in the Free French forces during the war, and their five children, and set herself up in New York. There she immersed herself in the jazz world and found what she wanted in the music and its society. Recognising that jazz musicians did their work largely in the face of public indifference, she devoted her resources to providing material assistance.

The nature of her relationship with Monk, the principal beneficiary of her largesse, has long attracted speculation. She adored his iconoclastic genius and, with the acceptance and complicity of his wife, Nellie, became the protector of a great pianist and composer rendered vulnerable by mental instability. A heroin bust in 1951 had cost him his cabaret card (the police permit that allowed musicians to work in New York clubs), and she fought to get it restored. When they were apprehended by police while she was driving him to an out-of-town gig in 1958 and a small amount of marijuana was found, she claimed it was hers; she was sentenced to three years in prison, and it took a two-year battle and the Rothschild family's legal muscle to get the case dismissed on a technicality in the appeal court. Monk spent the final, completely inactive years of his life in her house on the banks of the Hudson River, sharing the premises not just with Nica but with her scores of cats, which he destested.

At first strongly disapproving, particularly when the death of Charlie Parker in her hotel suite attracted tabloid headlines, her family gradually became more or less reconciled to her activities. After her death following heart surgery in 1988, however, it became clear that those who wished to investigate the life of this remarkable woman would come up against the wall of silence habitually erected by the Rothschilds even around the lives of their more orthodox offspring. Although individuals  including Nica's sister Miriam, an entomologist, and her brother Victor, a Labour peer and sometime MI5 operative  became well known, this is a family with a tradition of incinerating personal papers.

Even Hannah Rothschild, Victor's grandchild, found her path littered with obstacles when she set about the task of piecing together a biography that would go behind the familiar anecdotes. During her own childhood, the author had heard only passing mention of her eccentric great-aunt. In later years she arranged to meet Nica in New York and was given the full Jazz Baroness treatment: the Bentley, the jazz club, the whisky and cigarettes. But when it came to investigating the life, not even Nica's children were interested in fleshing out what had become a rather two-dimensional story.

Rothschild was undeterred and has completed a TV documentary, a radio programme and now a book about her intriguing relative. She examines the family's history and the inherent and acquired characteristics that may have laid the foundation for Nica's chosen modus vivendi, which is why The Baroness scores over Nica's Dream, a biography by the American writer David Kastin (WW Norton, 2011). While Kastin, who relies rather too heavily for comfort on Robin DG Kelly's fine recent biography of Monk, is more comfortable writing about jazz, Rothschild is unsurprisingly more at ease with the family, making her book less of a series of potted biographies of passing musicians and more of a rounded portrait.

Despite all this attention, aspects of Nica's story remain enigmatic. "Her story is our story," the saxophonist Sonny Rollins tells Rothschild. "It has to be told." To Miles Davis she was a "wonderful friend". But not everyone welcomed what she brought, and the poet and political activist Amiri Baraka (formerly LeRoi Jones) is withering in his condemnation: "She was a wealthy dilettante and a groupie. That is the kindest thing I could say, that she  had the wherewithal to be where she wanted to be and do what she wanted to do." It would have been interesting to hear the views of white musicians; in the absence of their testimony, we are invited to assume that she restricted her attention to artists of colour  something which, if true, would have been worth careful discussion in the context of jazz and race in an era that continues to reward examination.