Half believe that smartphones are acceptable to teens but few could agree on an exact age.
The research was carried out by YouGov on behalf of Firstsource Solutions, a global provider of business process outsourcing (BPO) services.
While 12 (17 per cent), 13 (17 per cent) and 16 (24 per cent) were the most popular ages to allow access to a smartphone, there was no definitive age.
And 92 per cent thought it was suitable for children under the age of sixteen to have a smartphone.
Twenty-six per cent of parents thought that sixteen and above were the most suitable ages for children to have a smartphone.
Where the majority were in agreement, though, was around primary school children, with 88 per cent agreeing that smartphones are not suitable for the under-10s.
In spite of this, though, more than one in ten felt that it was acceptable for children aged between five and ten to have a smartphone.
While smartphone-use may be seen as part of everyday life, parents remain concerned about the effect they may be having.
Firstsource’s research found that over two-thirds of parents – 68 per cent – are worried that their child’s concentration and learning abilities could be damaged by too much time online or on smartphones.
In London, the South West and the East of England, the figure is even higher, with three-quarters of parents concerned over the impact of smartphone use on learning.
The survey also showed that social media poses a particular dilemma for parents.
Sixty-three per cent of parents would be happy for their children to use social media below the age of sixteen.
Nearly three-quarters of parents – 79 per cent – would be happy for their 11-17 year-olds to use social media but, as with smartphones, there was little consensus about what age would be a suitable ‘entry point’.
The most popular ages that parents thought were suitable for giving young people access to social media were 14, 15, 16.
While only four per cent believe that primary school age children should be able to use social media sites, 15 per cent believe such sites should only be accessible to those aged 18 or over.
Iain Regan, Executive Vice President of Sales, Marketing and Client Services, at Firstsource Solutions, said: “For many of us, smartphones are part of modern life – and that’s increasingly the case among children too.
“Our research shows that there is both concern and confusion among parents.
“It’s unsurprising that the use of smartphones and social media by young people is a major concern, particularly as their use is only going to become more widespread over time.
“Recent headlines will only compound parents’ concerns. It is important to strike the right balance to give children the benefits of smartphones and social media while protecting their security.
“That’s why network providers, smartphone manufacturers and government need to continue to work together to give parents confidence on these issues.”