When the obstetrician Catherine Hamlin, who has died aged 96, first arrived in Addis Ababa, the capital of Ethiopia, in the late 1950s, she knew she wanted to make a difference.

She just did not expect it to be through decades of successful treatment of a type of birth injury she had assumed was an academic rarity, first at a general government hospital, then at a small hospital built by herself and her husband, Reg, and eventually through a national network of six hospitals, 80 midwifery clinics, the Hamlin College of Midwives, and a rehabilitation centre.

Obstetric fistulae occur in women who endure obstructed deliveries, for all the myriad reasons that these occur the world over: because the baby is breech, or too big, or tangled in the umbilical cord, or, if the mother is too young, because her body is unready. If there is no midwife or hospital, the labour continues for days, until the baby dies, shrinks and can be expelled; the pressure of labour tears the woman’s bladder, vagina, uterus, and often rectum as well. She finds herself incontinent, sometimes doubly so, and then, in many countries, shunned; women in this state can live alone and rejected for decades.

These days, obstetric fistulae are almost entirely avoidable and usually straightforward to fix, with life-changing effect. Catherine and Reg, both devout Christians, believed moreover in trying to heal the whole woman: “We don’t just treat the hole in the bladder,” as Catherine once put it, “we treat the whole patient with love and tender care, literacy and numeracy classes, a brand-new dress and money to travel home.”

No one given a tour of the Addis Ababa Fistula hospital, set on the lip of a steep valley in the south-west of the city, ever forgot the clean wide central ward based on the model Florence Nightingale pioneered, where one matron could survey everything at once.

The operating room was also in view of the ward, so, as Catherine put it in her 2001 memoir The Hospital By the River, patients “would be able to see people going in for surgery and coming out again, unharmed”. That surgery was performed by the Hamlins, and then, increasingly, by Ethiopian surgeons, and especially by an ex-patient, Mamitu Gashé, who arrived as a teenager and learned her formidable skills on the job.

Many of the women treated at the hospital had walked hundreds of kilometres to get there. Occasionally there was a child who had been raped, or, once, a seven-year-old caught in the crossfire of the Somali war. One patient took seven years to arrive – it had taken that long to beg the bus fare. All were treated free, paid for by charitable donations or, in the early days, from the Hamlins’ own salaries.

The hospital is surrounded by beautiful gardens, planted by Catherine; it is a bright, airy, calm place in which to recuperate.

Friends remember an unsentimental, warm woman with a quick and slightly wicked sense of humour; a person clearly incredibly busy who nevertheless made time for many thoughtful kindnesses; a practical woman who would go to great lengths to find solutions to seemingly intractable problems, of which, in her line of work, there were many.

They remember the white gloves in which she faithfully attended the local Anglican church and the steadfastness of her friendship – the Christmas cards she wrote without fail, however far-flung the friends, well into her 90s – and the loyalty and love she in turn inspired in everyone around her, especially in Yeshi Ayele and Birru Robi, who helped her run her home and cared for her for decades. They remember, above all, a person with a vocation to help those who, as she put it, had “suffered more than any woman should be called upon to endure”.

Born in Sydney, Australia, she was one of six children of Theodore Nicholson, who ran the family lift manufacturing business, and his wife, Elinor (nee Young). Catherine grew up in a large house in the suburb of Ryde, with a childhood of riding, camping, yachting and a spartan boarding school. She trained as a doctor at the University of Sydney and was wondering what to specialise in when she was interviewed for a job in obstetrics by Reginald Hamlin, the medical superintendent of Crown Street women’s hospital.

She chose obstetrics, and a couple of years later, in 1950, married Hamlin, who was 15 years her senior. They had one son, Richard. It was a difficult delivery further complicated by a serious blood disease and Catherine being knocked down by a bus when she was seven months pregnant.

They worked together in Sydney, London, Hong Kong and Adelaide before deciding they needed to make more of a difference in the world and in 1959 answered an advert in the Lancet, for someone willing to set up a school of midwifery at the Princess Tsehai hospital, Addis Ababa. Named after a daughter of Emperor Haile Selassie who had worked as a nurse in London during the second world war, then died in childbirth, it was built and funded by his longtime supporter, Sylvia Pankhurst, who was living in Ethiopia.

The Hamlins found themselves living, and thriving, in a world where a day could span a personal visit by the emperor, the delivery of a royal baby, an obstetric emergency, then an attempt to fix the fistula suffered by a destitute young girl.

The couple practised in peacetime and under gunfire, as in the 1960 coup that threatened to topple the emperor. Having asked the emperor’s personal permission for land, and raised all the money to build it themselves, they declared their new hospital open in 1974, the year the emperor was deposed in what became a violent revolution.

Over the next decades they operated on more than 60,000 women. An increasing part of their work turned into fundraising all over the world, a task Reg, a gifted speaker, was especially good at. When he died in 1993, Catherine, who was less comfortable with this public role, took over, making, at one point, an unlikely friend of Oprah Winfrey, who personally gave her $450,000 (a year’s running costs); viewers of Oprah’s TV show later raised a further $3m.

Catherine was made a Companion of the Order of Australia in 1995, and awarded the Australian Centenary medal; she was designated an Australian Living Legend, and, after popular demand, a Sydney ferry was named after her.

In 2009, she was given the Right Livelihood award; she was also nominated, twice, for a Nobel prize. In 2012, she became an honorary Ethiopian citizen and in 2019 was given an Eminent Citizen award in recognition of her lifetime of service to the women of Ethiopia.

She is survived by Richard, her grandchildren, Sarah, Paul, Catherine and Stephanie, her great-grandchildren, Thea and Luca, a sister, Ailsa, and brothers, Donald and Jock.

• Elinor Catherine Hamlin, obstetrician, born 24 January 1924; died 18 March 2020