Mums and dads told researchers they were seriously lacking in confidence when it comes to interacting with their own offspring.
Some 13 per cent felt anxious about play, while 17 per cent admitted buying toys and video games for their children to take the pressure off themselves, the survey revealed.
Now play campaigner Adrian Voce called on the government to develop a national play strategy.
Researchers for the drinks brand Ribena questioned 2,000 parents of children aged from three to 15 across the UK for its Ribena Plus Play Report.
The report coincides with another survey by the National Trust, which is campaigning for more outdoor play, such as climbing trees and building a den.
The Trust has produced a list of 50 things children should do before they're 11 years old.
The Play Plus Report that 59 per cent of fathers and 42 per cent of mothers were so busy that they had fewer than five hours a week to play with their children.
Just under a third of parents said they felt guilty for playing with their children instead of doing housework.
Mr Voce told BBC News: "Society has got its values back to front if parents feel guilty for playing with their children instead of doing chores.
"Playing with your kids is just as important as any aspect of looking after the home."
His advice to parents is: Don't be so anxious. Lose the ironing for half a day.
"Play is one of the most simple and basic activities. If it feels good and the child enjoys it, then that's the way to do it."
Play tips include making musical instruments from tin cans, going on a nature trail in the local park and building a dressing-up wardrobe from old boxes and pillow cases.
The National Trust's "50 things to do before you're 11" campaign has recruited experts to encourage families to visit National Trust properties.
Some of its "play musts" include:
Climb a tree
Roll down a big hill
Camp in the wild
Build a den
Skim a stone
Run around in the rain
Fly a kite
Dam a stream
Catch a crab
Does this ring true for you? Do you feel at a loss for how to play with your child?