An edition of Kenneth Grahame's The Wind in the Willows, dedicated to the daughter of Sir Arthur Quiller-Couch, who was thought to have been the model for the character of Ratty, sold for 10 times more than expected

A first edition of Kenneth Grahame's children's classic, The Wind in the Willows, belonging to the daughter of the man thought to have inspired the character of Ratty, has been sold for £32,400 — a sum 10 times higher than anticipated.

The book, which was sold by Bonhams at auction in London yesterday, is inscribed "To Foy Felicia Quiller Couch from her affectionate friend Kenneth Grahame, Oct. 1908". Quiller-Couch was the daughter of the Cornish author Sir Arthur Quiller-Couch, a friend of Grahame's who often had the author to stay at his house, The Haven at Fowey. Like Ratty, Quiller-Couch enjoyed boating, and is thought to have been Grahame's model for the character of the talkative Water Rat, who tells his friend the Mole that "there is nothing — absolutely nothing — half so much worth doing as simply messing about in boats".

Grahame began The Wind in the Willows as a bedtime story for his son Alistair, continuing it in letters written to him while staying at Fowey. The arrogant but lovable character of Mr Toad is said to have been partially inspired by Alistair, an adventurous boy who would escape from home when young and lie in the road waiting to be run over by a car. "We can see in this possibly the source of Toad's fascination with motor cars," writes David Stuart Davies in an afterword to the Collector's Library edition of the novel. "'The real way to travel!'" cries Toad. "'Here today — in next week tomorrow! Villages skipped, towns and cities jumped — always somebody else's horizon! Oh bliss! Oh poop-poop! Oh my! Oh my!'"

By Christmas 1907 the book was finished, and Grahame sent it to publishers in the UK and the US who both turned it down. Methuen eventually agreed to publish the book but paid Grahame (who worked in banking) no advance, and the book was met initially with critical disdain. One very literal review, in TP's Weekly, said it would "win no credence from the best authorities on biology"; writing for The Bookman, Arthur Ransome called it "a failure, like a speech to Hottentots made in Chinese".

Its staunchest advocate was, however, an important one. Theodore Roosevelt, then US president, wrote to Grahame in 1909 to tell him that he had "read it and reread it, and have come to accept the characters as old friends". Roosevelt eventually persuaded US publisher Scribner to take it on. Another fan was AA Milne, who adapted it into the play Toad of Toad Hall, and wrote in an introduction to an edition of the novel that "one does not argue about The Wind in the Willows". "The young man gives it to the girl with whom he is in love, and if she does not like it, asks her to return his letters. The older man tries it on his nephew, and alters his will accordingly," said Milne. "The book is a test of character."

• This article was amended on 25 March 2010. In the original it said that The Wind in the Willows was finished in 2007. This has been corrected.