The life of Florence Nightingale falls neatly into two acts. During the first, she stayed in the drawing room of her family's country house, dreaming about doing something else; during the second, she stayed in the stark bedroom of her own house, wishing she could be somewhere else. For her first 34 years, she wanted to nurse the sick and was prevented from doing so by her disapproving parents; during her last 54 years, she was herself the invalid. There was a two-year interval in the middle, 1854-56, when she became famous as the Lady with the Lamp, ministering, at the Barrack Hospital in Scutari, to the dying and wounded British soldiers of the Crimean war.

The stillness of Nightingale's life (1820-1910) always comes as a surprise; apart from her time in the Crimea, the action took place inside her fabulously energetic mind. During her years at home, this constant “dreaming” became, she said, “like gin drinking”. The longing to nurse was “eating out my vital strength” and came close to destroying not only Florence but her mother and sister, too. Her most important work, however, was done not when she finally escaped England, but after she returned to London and, disabled by what Bostridge convincingly shows to be a chronic form of brucellosis, took to her bed. From here she organised, among other things, the Nightingale School of Nursing at St Thomas's hospital, and a drainage and sewage system for India.

It also comes a surprise to realise how much she wrote, although Virginia Woolf described Cassandra, Florence's landmark essay on the condition of women, as more screaming than writing. As a correspondent, she shone; she could, as one reader said, “dash off 10 pages of advice on steam boilers, 13 pages on the use of Parian cement of hospital walls, 12 pages on floor polish, and six pages on tea making”. She could also find a hundred ways to describe the deadening effects of melancholia. “I feel myself perishing when I go to bed,” she wrote in the years before she nursed; “I wish it were my grave.”

Florence sent so many letters throughout her life that it's a wonder she had time to soothe any fevered brows; even in the depths of delirium in Scutari, when she was too ill to speak, her pen was scuttling across the page. Writing, whether letters, Notes on Nursing, Notes on Hospitals, The Sanitary Progress in India or her great work of religious philosophy, Suggestions for Thought, was part of her rage for organising chaos, internal and external. Her skills lay less in nursing than in administration and numbers; she was happiest when she could demonstrate the causes of mortality in pie charts, or “coxcombs” as she called her colourful statistical diagrams.

In order to uncover who this extraordinary woman really was, Mark Bostridge has had to sift through 150 years of mythmaking. For some, Florence was the ideal of womanhood: silent, nurturing, sacrificial, a prototype Princess Diana. For others, she was rather different - closer, as Bostridge observes, to Margaret Thatcher. The poet Arthur Hugh Clough, married to her cousin, Blanche, described Florence as “having an unsympathetic, unloving sort of temper...une tête forte, lucid, and not rich, though intelligent; not creative, arithmetical, ‘positive', matter of fact; a little arid, not tender... a little hard”. Lytton Strachey, who began the process of demythologising Florence in Eminent Victorians, called her in private “a terrible woman”, adding that she was “a complete egotist...and I don't think really intelligent”. Her elder sister, Parthenope, concluded that the reason she could not see Florence clearly was because “I have lived too passionately in her life”.

The relationship between Parthenope and Florence, brilliantly evoked by Bostridge, verged on the vampiric. Parthenope's feelings towards Florence, Bostridge writes, “had become fixations in her mind, dominating her with mounting intensity that can only be described as monomania”. Florence's strength, her belief that God had given her a purpose - she had a visitation when she was 17 - made Parthenope weaker; the sisters could not exist in the same place at the same time. Parthenope was drained by Florence's unhappiness at home, by her furious ambition, by the size of her ego; Florence was baffled by the absence in Parthenope of “that wanting something” which was her own driving force. When Florence was not there, Parthenope became ill - a friend described Parthenope's sense of bereavement as being similar to the loss of “a lover”. When Florence was there, Parthenope became ill. An insightful doctor ordered “the most crucial and necessary step of her separation from her sister”. When Parthenope became engaged, aged 39, she wrote that she “never thought to marry anyone but Flo”. Marriage released her from the curse of living too passionately in Florence, but Florence's bitterness against the institution of the family - a “thumbscrew...an instrument of torture” - became what Bostridge calls a “festering wound”. “What have my sister and mother ever done for me?” Florence exclaimed when she returned, a heroine, from the Crimea. “They like my glory...Is there anything else they like in me?”

And is there anything to like in them? Earlier biographers have thought not, but Bostridge paints a moving picture of Parthenope while challenging the received image of Fanny Nightingale, Florence's mother, as a small-minded woman motivated solely by convention. Fanny was, Bostridge shows, endlessly struggling to understand the hurricane in the house. When Florence first left home in her thirties, to work at the infirmary in Kaiserswerth, on the Rhine, she received from her mother an extraordinary letter that encouraged her to “take time, take faith & love with you, even though it be to walk in a path which leads you strangely from us all”. Fanny asked her daughter to “be merciful” to her family, “& not lay upon us more than we are able to bear”.

Bostridge also suggests that Florence's steadfast refusal to marry Richard Monkton Milnes (“to be nailed to a continuation and exaggeration of my present life, without hope of another...would seem to me like suicide”) was not as straightforward as has been supposed; she may have been on the brink of changing her mind when he “seems not to have understood her”, as her Aunt Mai explained to Florence's frantic mother, “to have supposed her still to refuse him, & married another”.

“Such a long journey,” one of her former nurses mused on reading Sir Edward Cook's Life of Florence Nightingale (1913), “with its sheltered places, its highest mountain tops early on the way, & the long long populously level plains to the end.” It is hard to imagine how one might improve upon Bostridge's masterly understanding of the costs, trials and triumphs of making that journey, not only for Florence but for all those friends, family, ministers, soldiers, nurses and servants who accompanied her. Whether his subject is sewers or psyches, mothers or mysticism, his understanding is complete and his prose crisp and clear, while his organisation of the vast body of material such a long long journey involves would satisfy the exacting standards of even Florence Nightingale herself.

Florence Nightingale by Mark Bostridge
Viking £25 pp671

Times Recommends

• The 100 Best Books of the Decade
• The Times picks the 50 best paperbacks of 2009
• The conversation: James Ellroy