Only one in eight fathers is the main reader for their child, and a quarter of those who aren't say they work too late to take the lead on reading.
A study, commissioned by reading charity Booktrust and carried out by Opinium, found that only 13 percent of men are the main reader with their child, with 25 percent saying working late means they do not have time to read to their children.
Findings also showed that many dads believe reading is a "female domain" and that mothers work in "isolation" instead of sharing practices.
The research also indicates that fathers prefer reading to daughters than sons - reading to them longer and more often.
Viv Bird, Booktrust chief executive, said: "The most crucial thing for dads to understand is that if kids see their dads reading they're more likely to enjoy it themselves.
"There is evidence that boys are slipping further behind girls in reading - and this emphasises how important it is that dads are positive role models to their sons as well as their daughters when it comes to reading."
Research suggests that a father's involvement in their child's early reading boosts academic success and leads to improved social and emotional wellbeing.
UK beind America
In response to the Booktrust findings, the Duchess of Cornwall and author James Patterson have launched a campaign to 'Get Dads Reading'.
They visited a dads' reading group in Greenwich, London. At present, only around 10 percent of parents attending formal literacy events for children are dads.
Patterson said: "If we can get children reading and enjoying books, we open up a whole world of possibility to them. I believe that dads have a huge role to play in encouraging their children to read.
"We need to give fathers the support they need in reading to their children. If I can help dads to understand their role in making books and reading more important in children's lives, I'll be a happy man."
Speaking to the dads' reading group, he added: "We are here to save lives, that's my role, because if you cannot read your life will be severely disadvantaged.
"This is not about reading Charles Dickens or Shakespeare but learning to read with confidence and if you can do that you can make your way through school, college and work.
"If you cannot read you just look at school and think 'this is hopeless' and so you reject it. America is ahead in getting kids to read, the UK is behind America - something's going wrong here."