Hello to sailors, sapphists, and a topaz as big as a fist

Tamara de Lempicka worked with precision. "My paintings are finished from this little corner to this little corner," she wrote. "Everything is finished." She is best remembered for the portraits she did in Paris in the 1920s, of assertive female nudes with limbs entwined and faces fused. They startle because of the contrast between clarity of form and ambiguity of relationship.

Legend has it that she herself was a helluva girl. No previous biography has appeared. The reason for this is a lack of letters, journals and diaries, by or about her. Laura Claridge is undeterred. For source material she has used Lempicka's prosy autobiographical pieces, five books of press clippings about her shows, anecdotes from her daughter Kizette Foxhall, what must have been hours on the phone with embalmed White Russian émigrés who perhaps brushed shoulders with "one of the century's most dramatic and imposing personalities", and "Tamara's ghost" - who encouraged the enterprise with "a sudden guttural chuckle" in the author's ear.

God knows what the ghost was laughing about. It ought to have insisted on a better book than this. Claridge's structure is from birth to death. Between these vague events (was it 1895 or 1898, and did Lempicka's nurse murder her, or not?) all is speculation, hearsay, gush and irritation.

No "ordinary woman", we are told, "could stare at a man's trousered crotch with Tamara's icy elegance, a gaze that the seductress would follow with a long drag on her ebony cigarette holder." How on earth did Laura Claridge know? I turned to the footnote (101 of chapter 3). "Told to the author by the very gracious Alexander Chodkieweitz in a lengthy, delicate and sometimes awkward phone conversation."

Chodkieweitz also remembered that Lempicka's "favourite sexual activity was to be caressed over her very colourful, very excitable nipples and genitals by a beautiful young woman, while she performed similar activities on the most handsome sailor in the group. After such nocturnal stimulations, she returned home full of confidence and insight - and cocaine - and in a frenzy painted until six or seven am. After several hours of sleep and a quick breakfast with Kizette, she resumed her daily routine of art classes and café socialising before preparing to begin her night life anew."

Then there is testimony from "the cynical George Schoenbrunn", who told the author that Lempicka smelled and left derisory tips in four-star restaurants. And Countess Maria Suzpuchiana who, from the Hotel Capri in October 1997, revealed that Lempicka went to seedy Paris night-clubs 70 years previously "fondling quite openly a beautiful working-class boy one night and a girl the next". Such anecdotes lead Claridge to assert that "no one could fetishize sex or orchestrate desire as well as [Lempicka]".

This is one way of writing biography. I searched the tosh for what might be true about Lempicka, beyond the strength and presence of her work, insufficiently represented here with only 16 plates. She was born in Moscow of Polish and Russian/Jewish parents. Her family name was Gorski. When she was 15 she met Tadeusz Lempiki. "When Tamara encountered Tadeusz at the costume ball in 1911, he had recently graduated from law school and was now free to frolic."

They married in 1917, then went to Paris with their baby daughter to escape the Bolsheviks. She determined to earn her living from her work. She copied Michelangelo and Botticelli to learn technique and in the Twenties painted those nudes that fill the canvas, without background, sculpted and hefty.

Her work was well-received in the 1925 Art Déco exhibition in Paris and in solo exhibitions. She seemed not to figure in the well-documented salon life of famous lesbians of the time, such as Gertrude Stein, Natalie Barney or Winnaretta Singer. She said she kept a detachment from café life because she was busy working.

Tadeusz left her in 1927. He went to Poland and married another woman. In Lempicka's valediction portrait he wears an overcoat and, hat in hand, turns his back on the city. After Tadeusz, she married Baron Raoul Kuffner de Dioszegh, who liked to hunt and attend to his land holdings. He bought her paintings between 1929 and 1933 and made her rich. Her modernist house in rue Méchain was of glass and chrome, with her initials woven into the cushions and a dining table for 20.

Before the Second World War, she and the Baron moved to America. In the Forties she painted still lives, inspired by Dutch and Flemish art, but little interest was evinced in them. She had solo retrospective exhibitions at respectable galleries, but seemed to move from painting to a leisured life.

Her Manhattan apartment cost a quarter of a million dollars in 1942 and was filled with gilt furniture and gold drapes. She liked her luggage to match her limousine, and in photographs looks like the vulgar rich. She had posh houses in Havana, Palm Springs, Manhattan and Paris. In old age she was a bit of a fright, bedecked in floral dresses with matching hats, and too much gold.

As for her moods and feelings, or who she was in any living sense, it is hard to know. According to Laura Claridge she "had a probable manic-depressive alternation in her mental cycles", "would sink into a panicked silence at the very mention of communism", and had "an intuitive response to beauty and the realm of the senses".

It is also not clear what form she gave to the decadence and lesbianism suggested by her work. It would be interesting to find out what was going on in the portraits she painted and in her private relationships.

The poet Gabriele D'Annunzio wrote saucy letters to her and gave her a topaz the size of a fist, but he did the same to Romaine Brooks and Radclyffe Hall. She had some kind of intrigue with Greta Garbo, but so did Cecil Beaton.

Laura Claridge states that one of Lempicka's models in Paris, Ira Perrot, "was possibly the major romantic attachment of her life", but divulges nothing of this relationship. Such assertions do not recreate Lempicka. But, whoever she was, glitzy people like Madonna and Barbra Streisand now pay millions of dollars for her bold, sensuous, forceful paintings.

Diana Souhami's 'Gertrude and Alice' and 'Greta and Cecil' have been republished by Weidenfeld