Two-thirds of parents and grandparents (67%) believe modern technology in the home distracts them from storytelling, while one-third (29%) are too tired for tales, another one-third (29%) get home from work too late and 22% are busy with other activities at home, the poll for Disney found.
Although just 30% of parents read to their children daily, 51% say story time allows them to spend time together and 47% know their children enjoy having books read to them.
The poll of parents and grandparents of children under six found mothers are most likely to read to youngsters (48%), followed by fathers (21%) and grandparents (17%). It also found 58% of women were read to as children, compared with 44% of men.
Television and radio presenter Zoe Ball, who is helping to launch Disney's Winnie the Pooh Storytelling Academy, which offers tips for reading to children, said: "When I was young, my dad [presenter Johnny Ball] would enthusiastically read tales of Winnie the Pooh, Piglet, Tigger and friends to me, and put on daft voices to really bring the story to life.
"These are memories which I treasure and now I can share those special bedtime stories with my own children."
A Disney spokeswoman said: "Parents and grandparents who face storytelling challenges such as a lack of confidence or distractions can go to pick up tips and tricks from our panel of experts.
"In this hyper-connected world we want to help them to keep the art of storytelling alive for the next generation via a whole host of media like iPad apps, audio books and the traditional hardback."