The creator of the classic children’s books The Tiger Who Came to Tea and Mog the Forgetful Cat, Judith Kerr, who has died aged 95, was unusual in being equally successful as a writer and an illustrator. She always claimed that she was “a very slow” illustrator and that her work was “more rubbing out than drawing”, but in a career that ran from 1968 to this year she created more than 30 books, mostly about Mog, all of which have remained in print and which sell worldwide.

The bestselling The Tiger Who Came to Tea (1968) was her first book. Characterised by its bold, naive-style illustrations and gentle anarchy, it tells the playful and imaginative story of how the everyday routine of a mother and her young daughter, Sophie, is disrupted by the unexpected arrival of a handsome stripy tiger. There is no panic; the tiger settles down to drink all the water and eat all the food, to Sophie’s delight rather than terror, before exiting politely. When father comes home he cheers mother and daughter up by taking them out to dinner.

An annotated page from The Tiger Who Came to Tea. Photograph: Dan Kitwood/Getty Images

Described as “a dazzling first book”, which would make children “scream with delicious pleasure at the dangerous naughtiness of the notion” by Antonia Fraser, one of the earliest reviewers, it was initially received as exactly what it was: a simple picture book that generated delight for children. Later, it was subjected to much analysis, with many assuming that the tiger stood for the Gestapo, who had so vividly interrupted Judith’s own childhood. It was a view she dismissed flatly; when chairing her at events across the country I frequently heard her say, in the nicest way possible, “It’s just the story of a tiger who came to tea. I made it up to amuse my children because we were bored and because their father was away filming for very long days at a time.”

It was also to entertain her own children that Judith wrote Mog the Forgetful Cat (1970), the first of what was to become an enduring and hugely successful series about Mog, who was based on the progression of cats she herself owned – the last being the subject of Katinka’s Tail, in 2017. Both in the stories and in the talks she gave to very young children, Judith was most amusing about Mog and her endearing and infuriating characteristics. She gave Mog the human traits she believed cats to have while managing never to detach her from her animal self. In 2002, Judith wrote Goodbye Mog. It was brave to kill off a much-loved children’s character, although she was resurrected for a charity tie-in with Sainsbury’s and Save the Children, in Mog’s Christmas Calamity, in 2015.

At the time of Goodbye Mog, and repeatedly in her later years, Judith explained to audiences that it was really about people, not cats, dying and she wrote it because she was thinking about her own death and those of her friends. She always managed to speak of it with a matter-of-factness, neither too sentimental nor too brusque, and always entertainingly. Soon after her 87th birthday she told an audience in Edinburgh that she’d had a dream about her own funeral and that after it her children had gone straight to McDonald’s. “I was furious,” she said in mock seriousness, amid much laughter from the audience, “that they had hardly waited until I was dead to start eating junk food!”

Judith Kerr wrote Mog the Forgetful Cat in 1970. It was the first of an enduring series about Mog based on the succession of cats she owned. Photograph: Rune Hellestad/Corbis/Getty Images

Judith adapted completely to the contemporary requirement of an author and illustrator to be a live performer alongside the quieter and more solitary challenge of producing the books. Always thoughtfully prepared and elegantly and beautifully turned out, she remained a lively and inspiring speaker until her death, taking part in festivals and bookshop events, where she charmed audiences from babies to grandparents with her dry humour, warmth and natural storytelling ability. She had been due to appear at Hay festival next week, to speak about her forthcoming book, The Curse of the School Rabbit.

She used her own life as the inspiration for most of her work, claiming that a story was never as good if she made it up from scratch. Her original audience, too, came from her own life; long before she wrote anything down, she told her children stories. She wrote the books that followed partly because her son, Matthew, was so dissatisfied by the books he was expected to read.

She also wrote her first novel for her children as a way of telling them about her childhood. “It was so different from the way they grew up that I wanted them to know about it, and I wanted also to explain that it wasn’t nearly as horrific as it sounded,” she said.

When Hitler Stole Pink Rabbit (1971) is a spellbinding mix of fear and hope, the story of a little girl escaping with her family from Germany and the Nazis told through a child’s eye, just as Judith remembered it. As it was for Judith herself, family warmth and the parents’ protective way of dealing with threat prevents it from being the frightening and fractured story it might have been. The subsequent volumes, The Other Way Round – renamed Bombs on Aunt Dainty (1975) – and A Small Person Far Away (1978), had less dramatic impact, but Judith’s fresh tone remained constant as she traced herself adapting to her new surroundings and growing up.

In the books and in life she showed surprising equanimity about the upheavals she had undergone and the reasons for them. She did not dwell on the difficulties of a childhood spent as an outsider, having to learn first French and then English, and not having the position and wealth into which she had been born. Instead, she always spoke warmly of the past and especially the way in which arriving in England had felt like coming home and being safe.

Born in Berlin, Judith was the daughter of the distinguished journalist and writer Alfred Kerr (born Alfred Kempner). As well as being Jewish, he was an outspoken critic of the Nazis from the earliest days, and late one night in 1933 he got a tip-off that he would be arrested in the morning. Despite being ill in bed, he fled immediately to Zurich and, after secret meetings about which the children knew nothing, his wife, Julia (nee Weissmann), a musician and the daughter of a Prussian politician, soon followed him into exile, accompanied by Judith and her older brother, Michael. From Switzerland the family moved to Paris, and finally to England in 1936.

From their comfortable life in Berlin, Judith’s family adjusted to living in a hotel in Bloomsbury, central London, without a steady income, surviving instead on kindness and charity. Although Michael was sent to a single public school, Judith’s education was more peripatetic; she went to 11 different schools in Germany, Switzerland, France and England (where she learned English from the governess of an American family who befriended her), before being sent briefly to a boarding school paid for by strangers.

Judith left school at 16 to train as a stenographer. During the war, she worked for the Red Cross, but was able to get back into education in 1945 when she won a scholarship to the Central School of Art. Afterwards, she sold some pictures and textiles while teaching at a technical college before working as a script editor and writer for the BBC, a job she was encouraged in by her husband, the scriptwriter Nigel Kneale, best known for his creation of the TV character Professor Bernard Quatermass, of the eponymous series. They had met in the BBC canteen and married in 1954. It was only after her own children had started school that she began what was to be her life’s work, creating stories and pictures in an upstairs study, often accompanied by her beloved Mog and subsequent other cats.

Judith loved to work and was skilful at adapting her output as she grew older by switching from ink to crayons and coloured pencils, which could be more easily rubbed out. She never lost her enthusiasm for the children who read her books or for their parents, many of whom came to her talks in the hope – always rewarded – of getting advice about how to turn their own ideas into stories. She never appeared to flag, despite long signing queues; but she never turned down a stiff whisky afterwards.

She was appointed OBE in 2012, for services to children’s literature and Holocaust education, and in 2016 was given a lifetime achievement award by the Book Trust. Last week, she was named illustrator of the year at the British Book awards.

Kneale died in 2006. Judith is survived by their daughter, Tacy, a special-effects designer on the Harry Potter films, and son, Matthew, author of the novel English Passengers, which won the Whitbread prize in 2000.

• Anne Judith Kerr, writer and illustrator, born 14 June 1923; died 22 May 2019