When the art collector Peggy Guggenheim moved into her Venetian palazzo in 1949 she installed Marino Marini’s The Angel of the City on the landing stage. You can still see the bronze statue today. It depicts an ecstatic equestrian, body arched, erect phallus pointing urgently at the tourists as they putter up and down the Grand Canal. Guggenheim claimed in her memoir that she had instructed Marini to ensure that the figure’s phallus was detachable so that, should a huddle of sight-seeing nuns happen to pass by in a vaporetto, she could nip out, remove the offending organ, and spare everyone’s blushes.

This anecdote is the kind of thing from which Guggenheim’s biographers, of whom there have been many since her death in 1979, tend to avert their eyes, embarrassed at the way their subject always lets herself down at crucial moments by talking dirty. In any case, they ask, how feasible is this, really? Marini, like all artists, took himself deadly seriously and was hardly in the business of knocking up strap-ons for his masterworks. And Peggy Guggenheim, a highly sociable hostess with many calls on her time, is unlikely to have spent her days hovering by the palazzo windows on permanent nun-watch.

It is also thanks to anecdotes such as this that Guggenheim’s memoir, which she republished in different versions over a period of 30 years, received a critical drubbing when it first appeared in 1946. Stuffed with sexual scenes involving the smelting heiress’s reputed 400 lovers, including a hairdresser, a ski instructor, Samuel Beckett, Max Ernst and several gay men whom she took on as a challenge, Out of This Century appeared to be, in the words of a shuddering New York Times, “worthy of tabloid headlines and recounted in tabloid prose”. The Chicago Tribune, aghast at the “nymphomaniacal revelations”, suggested that a more accurate title would be “Out of My Head”.

What bothered the Tribune, the Times and a host of other newspapers was the way that the sleazy prattle of Out of This Century tarnished the reputation of the woman who had a legitimate claim to be one of the great heroines of 20th-century art. For without Guggenheim’s sharp eye, personal pluck and frenzied determination – as the Germans marched into Paris she embarked on a mission to save a painting a day – it is quite possible that seminal works by Brâncuşi, Klee, Mondrian, Magritte and Kandinsky would have disappeared in one of the Nazis bonfires of “degenerate” art.

Having escaped with her stash to New York by the skin of her teeth, Guggenheim then set about discovering a new generation producing a new kind of art. Motherwell, Rothko, De Kooning and, most famously, Pollock were the men who, gusted along by her enthusiasm and financial doles, would go on to create America’s first art movement of international importance, abstract expressionism.

Francine Prose is a novelist and literary critic rather than a professional biographer, which may be why she is unwilling to fall in with the general perception that Out of This Century is an appalling embarrassment. Not that Prose proposes reading the memoir, with its fudges and wild boasts, as a documentary account of her subject’s life. Rather, she suggests, it cements Guggenheim’s reputation as a creative artist in her own right. By quite consciously disregarding calendar time, flaunting the unreliability of her memory, and breaking the conventions about what a woman could and couldn’t say about her own life and body, Guggenheim produced a piece of modernist prose that exhibited the same daring and originality as the art she loved to collect. Out of This Century, for Prose, is a (nominally) non-fiction equivalent of Nightwood, the strange, dream-like novel written by Djuna Barnes while she was staying at Guggenheim’s 1930s boho hang-out in Devon, Hayford Hall (remembered fondly by its many guests as “Hangover Hall”).

Still, whether or not Guggenheim’s writing really was “almost as good as Gertrude Stein”, as Gore Vidal insisted, it will always be the art that matters. Peggy’s Uncle Solomon had got in first with his stodgily named “Gallery for Non-objective Painting” in midtown Manhattan, which meant that, right from the start, Peggy’s collecting career was braided with oedipal competition (her real father had gone down on the Titanic). Her first gallery, in Cork Street, London, was named “Guggenheim Jeune” to make the point that the work collected here was different (fresher) from that of Uncle Solomon and his prissily defined non-objectives. The opening show, curated by Marcel Duchamp, featured drawings by Jean Cocteau done on bedsheets. The second was a one-man show of Kandinsky, his first in Britain.

Returning to her native New York in 1941, Guggenheim opened her new museum/gallery hybrid on West 57th. The spectacular space, designed by Frederick Kiesler, aimed to offer what today we’d call a multisensory experience. The artworks appeared to hover in the air thanks to a system of pulleys, a locomotive seemed to be rushing through the room courtesy of an audacious sound system, and lights were set on timers to shine first on one part of the room and then another. Everyone, from Jean-Paul Sartre to Gypsy Rose Lee, came to gawp at the novelty, and the serious ones stayed for the art.

This excellent short biography appears in Yale’s “Jewish Lives” series, and Prose is a subtle and attentive chronicler of the antisemitism that operated in her subject’s life. The Guggenheims and the Seligmans (Peggy’s maternal family) worked assiduously to be more like white Anglo-Saxon Protestants than the Wasps themselves, careful never to remind anyone of their origins. Nevertheless, as Prose recounts with mounting indignation, whenever any of Guggenheim’s friends, lovers, husbands, artists or acquaintances were feeling cross with her, usually because she hadn’t immediately offered to pay for their children’s schooling, a return ticket to Europe, or their girlfriend’s new studio, they would automatically make jokes about her parsimony. In a novel by William Gerhardie, she appears barely disguised as Molly, “a rich American” who is apt to complain that she isn’t as rich as people think. And in “The Cicerone” by Molly McCarthy, who claimed to be a dear friend, she is “Polly Grabbe”, a wealthy, expatriate slut who collects statuary and always puts on her glasses to scrutinise the bill in restaurants. This was, at least, marginally less cruel than the many other “friends”, business associates, protegees and, shame to say, biographers, who could never resist drawing attention to the size of the Guggenheim nose.

• To order Peggy Guggenheim go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.