Comparatively, just 10% found it difficult to get their children to complete their homework, 17.5% struggled to send them to bed and 19% faced a battle with healthy eating.
Carol Iddon, managing director of operations at Action for Children, said: "Technology is an often necessary part of the lives of children and parents alike, but it’s important to maintain a balance with other activities and quality family time.
"We know from our extensive work with families that strong relationships with parents build resilience in children, making them less susceptible to bullying or abuse outside the home, and encouraging them to speak to their parents about any fears or concerns."
Liat Hughes Joshi, author of 'How to Unplug Your Child', told HuffPost UK Parents, she concurs that this is "undoubtedly one of the biggest issues modern parents face", but it is important not to demonise screen time - as it's not all bad.
"Tech is clearly a big part of all our lives now and there's no getting away from that," she said.
"Indeed it has plenty of benefits for our children. So there’s no question of switching off altogether – they’d lose out on education, entertainment, information and, for teens, socialising.
"This should be about ensuring though that screens don’t ruin our ‘real’ offline relationships and don’t hamper our children’s social skills."
Martin Talks, author of 'A to Z of Digital Detoxing', believes part of the problem is that children are being introduced to screens at an increasingly young age.
"There is this rush to get children in front of screens at a young age," he said.
"Usually this is driven by a desire to keep children quiet rather than an aspiration that they be the next Zuckerberg. This is no better than drugging the child.
"We are effectively conducting a mass screen experiment on young people with no idea of the consequences."
Action for Children has published five tips to help families "unplug":
- Plan fun family activities that don’t involve technology.
- Create a weekly schedule on the principle of an hour of 'energy in' (technology use) equalling an hour of 'energy out' (other activities).
- Think back to your own childhood and play your own favourite games with your children.
- Identify the challenges your children enjoy in the video games they play and replicate them. Do they like games about sport? Encourage them to play the real deal in the park or go as a family to a local match. Are their favourite games puzzles or brain-teasers? Organise a board game night.
- Practice what you preach: when your children are having screen-free time, turn off your devices too.
Hughes Joshi believes it helps if you set a good example yourself. There's no point telling the kids off for staring at screens if your phone is permanently in your hand.
"I’d suggest looking close to home and ensuring you set a good example," she said.
"How many of us are glued to screens but then expect our kids to behave differently? Of course we might need to be online for work but when we don’t, ensure you’re a decent role model – don’t jump and grab your smartphone every time a message arrives."
"Parents need to ask themselves some tough questions about their own screen habits and how they have introduced screens into their children's lives," he said.
"If meal times are taken in front of the TV; if conversations are interrupted to glance at phones; if work emails are dealt with in evenings, weekends and holidays; how can parents expect their children to be any different?
"Parents should provide positive examples and positive alternatives. Try to kickstart the process with a digital detox break. Remove all devices - including the parents' - and enjoy other activities. Get the children involved in suggesting activities."
As well as digital detoxes Hughes Joshi also advises setting up tech time rules that apply to everyone - adults included.
"A set of family screen time rules can be very powerful," she said. "These should be set together and can involve the children.
"Examples would be no screens during meals, perhaps not for the last hour before bedtime (screen glare is associated with sleep problems) and no tech when there are visitors (other than perhaps sometimes when they have friends over).
"Finally, try not to buy younger children their own gadgets – they really don’t need a tablet or smartphone aged five. Hold off as long as you can and stick with ‘family’ tablets etc. because this makes it easier to keep an eye on what they are doing and also to take it away because it is not ‘theirs’.
"Most of all don’t be afraid to stand firm – you’re the parent and if you think screens are getting too much, take them away, set firmer limits, do what you need to even if it causes a strop or tantrum.
"It’s not easy but if you believe it’s the right thing for your children and they’re getting tech overload, it’s worth it."
Lucy Gill, director of apps and technology at Fundamentally Children, also has some advice on separating children from their devices without a row erupting.
"Give them warning when the 'end' is nearing so they can learn to find a natural end point," she said.
"You'd be pretty cross if you were in the middle of something and someone came along and turn the tablet/computer/TV off, warning is important and will help them self-regulate.
"Initially try to encourage them away with suggestions of what they might do instead.
"It shouldn't always be a parents role to suggest or steer play, but if you're struggling to get a child off a tablet then suggesting something else they will enjoy is a good motivation and helps them recognise the importance of a balance too.
"As soon as possible encourage children to regulate their own screen time.
"Talk to them about why you're worried about them spending too much time on it and encourage them to find a balance for themselves.
"This makes them feel part of the process and sets them up well for later life."
Talks adds that while it's important mums and dads take these steps to limit the amount of time their children spend looking at screens, he also believes responsibility doesn't lie solely on parents.
"Companies need to take a measure of responsibility too," he said. "Smartphones should carry health warnings and usage guidance. Like any addictive substance."