The girls adored hearing the rabbits' adventures, set in the Hampshire countryside. And at their request, aged 52, he put pen to paper.
Six publishers rejected it, all concerned older children would not want to read about rabbits and that its dark themes were too "adult" for younger children.
But Adams maintained it was a tale for all, from those "aged 8 to 88", and he was proved right when it was published in 1972.
It went on to become a best-selling classic and was adapted into a 1978 cinema hit, directed by the author's good friend Martin Rosen.
Adams later admitted the depiction of his rabbits was not quite as he had imagined.
But the animated film and its accompanying theme song Bright Eyes, sung by Art Garfunkel, was at No. 1 for six weeks in 1979, and became an enduring family favourite.
A remake of the film by the BBC and Netflix was announced in April and it is expected to air over four one-hour parts next year.
Adams stumbled into a career as a writer. Born May 9, 1920, and raised in Berkshire, he enrolled at Worcester College in Oxford in 1938.
When war broke, he enlisted in the Royal Army Corps.
He returned to complete his studies, gaining a degree in modern history, before finding work as a civil servant in the ministry of housing and local government in 1948.
Adams married his wife Elizabeth in 1949, his neighbour's daughter, whom he had met when she was 17. In his 90s, he still referred to her as the "the girl next door".
The success of Watership Down allowed Adams to become a full-time writer, penning several novels, including Shardik in 1974, a fantasy novel about a wounded bear. He described Shardik as as his favourite work, but it failed to replicate Watership Down's success.
The author's interest in animals extended beyond his literary works and he was president of the RSPCA from 1980 to 1982.
In 1996, 24 years after his first novel, Adams published its sequel, Tales From Watership Down, a collection of 19 short stories that allowed readers to rekindle their relationship with the much-loved characters.
In his later life, he expressed regret that he had not realised his talent sooner, saying: "If I had known earlier how frightfully well I could write, I'd have started earlier."
Adams spent his later years with his wife, retaining a passion for reading and writing.
Deputy Whitchurch Mayor John Buckley said "the town will remember him for his book Watership Down".
"He will be sorely missed."
Buckley said steps had already been taken to remember Adams by requesting that roads in a new development are named after him and the characters in Watership Down.
The family's statement announcing his death quoted a section of the book.
It read: "It seemed to Hazel that he would not be needing his body any more, so he left it lying on the edge of the ditch, but stopped for a moment to watch his rabbits and to try to get used to the extraordinary feeling that strength and speed were flowing inexhaustibly out of him into their sleek young bodies and healthy senses. "You needn't worry about them," said his companion. "They'll be alright - and thousands like them."