The 84-year-old invented the characters of the Wombles of Wimbledon Common, who became household names in the 1970s.
She died on Christmas Eve night in the Mignot Memorial Hospital on Alderney in the Channel Islands after suffering heart failure, her son Marcus Robertson said.
The name The Wombles came from a mispronunciation by daughter Kate when she was a child on a Boxing Day stroll, and spoke of "Wombledon Common".
At home that same day, Beresford made out a list of names for characters, and soon Uncle Bulgaria, Tobermory and Orinoco became world famous.
The first Wombles book was published in 1968 and, after it was broadcast on Jackanory, the BBC decided to make an animated series.
The Wombles' motto "Make Good Use of Bad Rubbish" and their passion for recycling is widely seen as being way ahead of its time.
Children everywhere were inspired by it, starting Womble clearing up groups across the country. Music from the show, by Mike Batt, even made it into the pop charts.
Within 10 years Beresford wrote more than 20 Wombles books, translated into more than 40 languages, dozens of TV films and a stage show.
She was awarded an MBE for her services to children's literature in the 1998 New Year's Honours List.
Beresford's father was the writer JD Beresford, a successful novelist who also worked as a book reviewer for many newspapers, and her parents' friends included famous figures literary such as HG Wells, George Bernard Shaw, John Galsworthy and Somerset Maugham.
After 18 months spent as a Wren, Beresford began work as a ghost writer, specialising in writing speeches, including some for Conservative MPs, and met Sir Winston Churchill.
She began training as a journalist and wrote radio, film and TV columns and worked for the BBC as a radio reporter.
In a November 2010 interview with the BBC, she described the moment her daughter inspired the creation of the characters.
She said: "It was my daughter who said to me 'oh ma, isn't it great on Wombledon Common?' and I said 'That's where the Wombles live.'"
"Over Christmas I had to keep the children quiet as their grandparents were visiting, so on Boxing Day, after they left, we got in my car and went to Wimbledon Common.
"The three of us ran backwards and forwards screaming at the top of our voices, and it was my daughter who said to me, 'Oh ma, isn't it great on Wombledon Common?' and I said, 'That's where the Wombles live.'"