One in 10 parents (11%) said children should be aged 16 or over before they have their first mobile phone.
Cheryl Wheldon, president of head teachers' union NAHT Cymru, said the results of the survey reflected her experience as head teacher at Coedffranc primary school in Neath.
"I think these figures are right," she said. "The majority of the children in the 7-11-year-old group here have got a mobile phone, or access to one."
Ms Wheldon explained that her school had experienced "some issues arising from bullying through text messages".
There are lots of ways in which a parents can set down guidelines for their children
Suzie Hayman, Parentline Plus
"Eighteen months ago we had a nasty incident with 10-11-year-olds texting each other quite nastily after school.
"It was quite a difficult issue to address. I spoke to the pupils and their parents and it was only through their help that I could deal with it."
For this and other reasons, she explained, Coedffranc has banned pupils from bringing in mobiles.
"The policy at our school is that they should not bring them in. The issues are theft, misplacement, damage and, more to the point, it's a question of mobile phones going off in the middle of a lesson," she said.
"Young children having a mobile is a good thing and a bad thing. Safety does come into it.
"If I was the parent of a 10-year-old I might consider buying them a mobile phone so that I could get hold of them. At the end of the day it comes down to reasonable use."
BBC Wales asks at what age a child should have a mobile phone
Ms Hayman said her organisation gets "a lot of calls from parents" on the subject of children having mobile phones.
"It's generally considered appropriate for a child to have a mobile at secondary school level," she said.
"Young people are slightly more independent at that age, and have to stay for after-school clubs and so on. Parents want to know they have a link to them."
However, Ms Hayman added that she would encourage children in divided families to have a mobile phone at a younger age.
She said: "If a child's father, for example, does not live with the family, then having a mobile can allow the child to regulate when they get to speak to him, and that is a positively good thing; very much so with children under 10.
"Clearly there are issues about being mugged, running up enormous phone bills and cyber-bullying, but what we do is help parents manage these issues rather than just banning the use of a mobile phone.
"There are lots of ways in which a parents can set down guidelines for their children."
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