Hazel, Fiver and Bigwig, his freedom-fighting rabbits, soon made their way into the leporine hall of fame alongside Peter Rabbit, Br'er Rabbit and the Velveteen Rabbit. Adams left the civil service to write full time. He was 54, and too old to take up a position in the literary establishment.
"I'm a very naughty boy in that respect," he says. "I don't really live in the literary world. I mean, I ought to know them all but I don't. They don't know me very much. Real authors are continually meeting each other, aren't they?"
Adams is 94, a beady owl with a plume of feathery white hair sitting in a high-backed armchair in his snug Hampshire home, where he lives with his wife. The book that made his reputation is being republished in a handsome hardback edition by Oneworld. A copy sits on the table beside him, and its author seems chuffed to bits. "I think it'll go on selling forever."
Did he really just make it up as he went along?
"The stories I told in the car had nearly always been shaped and cut and edited by myself for oral narration. When I was lying down to go to sleep in the evening I would think out the bit of story I was going to tell the girls the next day."
He is especially pleased because Shardik, Watership Down's successor, is getting the same treatment (although rather rueful about a horrible typo: "Ortelga" is reproduced on every page of the first section as "Ortlega"). Does he think Shardik, his mythical saga about internecine wars with a godlike bear at its heart, had a fair hearing when it was published 40 years ago?
"No! They were expecting something like Watership Down. And they didn't get it. They got this rather difficult and savage novel. Shardik is a hard book to read. A lot of people have said that. They had to struggle with it. But I like it and I read it often."
What inspired the book? "I can't think of any experience of mine that would give rise to Shardik. I'm so old my memory is a bit weak," he concedes.
Indeed, he is inclined to speak of the long dead as still alive. Who is his favourite contemporary author? "Mary Renault," he offers. She died in 1983. The greatest English novelist? "Evelyn Waugh has had a long and successful career, hasn't he? This blithering Catholicism is a bit annoying."
Adams takes the view: "A book is a book is a book, and you write what has to be written to tell the story properly. I never consider the readers. I was allowed to read anything I liked when I was little and I liked all sorts of things that I shouldn't have been reading. I stumbled on frightening literature. Poe. The Hound of the Baskervilles. Algernon Blackwood's Ancient Sorceries."
His daughters must have sometimes been scared witless by the time they got to school. Was he aware of his daughters' terror as warrens were gassed and rabbits snagged in barbed wire? "I think I was, really. Perhaps I didn't water it down enough."
Shardik was followed by The Plague Dogs, about three dogs on the run from a vivisection laboratory. "I was expecting a wide success for The Plague Dogs," he says. It was well received but not a runaway hit.
Adams knows that his debut will be his epitaph. "But I'm not the only man who has - I wouldn't say - suffered. Kenneth Grahame wrote plenty of other things but they're under the shadow of The Wind in the Willows."
His most recent novel - Daniel, about a young black slave in the era of abolition - was published in 2006. "It was in my mind a failure because I was trying to do what I don't do - write a grown-up novel for grown-up people. Well, that's not my line. I'm a fantasist. I live in a world of fantasy, really."
Does he still write? "Oh yes, I'm writing all right."
What? "Shan't tell you," he says with a twinkle. He then relents and reveals he's writing about an ordinary boy who finds himself on a ship engaging with the Spanish Armada.
"That is a very good field for fantasy. You've got to get it right, mind. I've got a great respect for history. I read history at Oxford. His passion for make-believe was stoked by the sort of country childhood that no longer exists. He was much the youngest of three children and, in 20s Berkshire, had to entertain himself. "I made up a kingdom of my own. And I had several devoted followers and we did all sorts of things together. It was all imaginary."
In 1939, when his studies at Oxford were interrupted, Adams did his best to avoid engaging directly with history. He opted for the Royal Army Service Corps. He says he shares his DNA with the rabbit Fiver - "rather timid and not much of a fighter, but able to contribute something in the way of intuitive knowledge".
And to complement that intuitive knowledge, has age brought wisdom? "I like to think I've profited by experience and know a thing or two, as they say."
Would he subscribe to the view that things aren't what they used to be? "No, just the reverse. I think things have been improving all the time. It's a much freer society, to the point where one might feel this has gone a bit too far. I mean, before the War you were expected to behave yourself sexually. You don't have to now. And I think that often has very bad results. For example, the divorce rates. This leaves children in a sad state."
Watership Down was created, he says, out of a desire to be a constant parental presence - doing the school run himself before heading to work. "I've got a thing about that. Parents ought to spend a lot of time in their children's company. A lot of them don't, you know."
So how far is he on this new novel? "Oh, it's still in my mind."
Is he confident of finishing it? "No, I'm not! I may die at any moment. I'm 94. I've got to write or I wouldn't know what to do."
Does he fear the end? "We all do, don't we? Religious people, clergymen, and so on, may look forward to death as coming into another world. But I don't. I don't want to die but I try not to let it make me unhappy."
Watership Down and Shardik are published by Oneworld.
