Based on responses from 106 councils, the Association of Directors of Children's Services found that 11 per cent of home-schooled children are known to children's social care either currently or historically.
In addition, 18 per cent are known to wider children's services, meaning just under a third of home-schooled children have had some contact with children's services.
The survey also found that the number of home-educated children has increased significantly in the past two years. The ADCS calculates that there are now 57,873 home-schooled children across England this year, compared with 45,500 in 2017 and 37,500 in 2016.
The ADCS said the growth is likely down to greater awareness of home education, rising birth rates and improved council record keeping.
It is keen for councils to have stronger powers to intervene if they believe home education offered to children is unsuitable. School attendance orders (SAO) requiring a child to return to school can be used. But in its July response to a government consultation on home education, the ADCS said these were weak and need to be strengthened.
The survey shows that in 2018 a total of 515 SAOs were issued relating to home schooling, compared with 258 in the previous year's survey, which involved 112 councils.
The ADCS is further concerned that schools are "off rolling" challenging pupils by encouraging parents to take up home schooling.
The survey also found that the most common reasons given by parents or carers for home schooling was dissatisfaction with a school, with health and emotional reasons the next most common factor.
"Education is a fundamental right for all children and young people and we absolutely recognise that parents have the right to educate their children at home," said ADCS educational achievement policy committee chair Debbie Barnes.
"Where they opt to do so we want this to be a positive experience for both children and their parents, one that ultimately equips children to meet their own personal goals and aspirations. We believe this is best achieved when parents and local authorities recognise each other's rights and responsibilities, and work together.
"However, if the learning experience provided in the home does not meet children's needs, when schools are using home schooling as a means to illegally exclude children with special educational or behavioural needs, when parents use home schooling as a means to avoid attendance fines or as a cover to send their children to illegal schools, that's when we worry."
She added: "We know from our survey that the numbers of children being home educated have increased year on year for the past five years, this is only the children that we know of.
"There are likely to be many more children being home educated who are hidden from sight. We have no way of assuring ourselves that they are safe and receiving a good standard of education at home. This is not good enough."
Ofsted chief inspector Amanda Spielman has also raised concerns around home schooling and is calling on the government to bring in a home education register, that can be run by councils.
Speaking at the National Children and Adult Services Conference this week she said children outside mainstream education can be a target for gangs, particularly those looking to exploit children as part of so-called "county lines" drug distribution networks between urban and rural areas.
Another concern is that parents are becoming home educators "under duress and the threat of expulsion".
"The vast majority of home educators are well-intentioned and do a good job," said Spielman.
"But just as some schools struggle to cope with certain pupils, some parents struggle, too. They mostly aren't qualified teachers and their child may have complex needs."
"The crux of all this is that it becomes incredibly difficult, for you, for local authorities, to know whether children are safe and getting a decent standard of education.
"That is why we have lent our weight to calls for a register of home education, run by local authorities, which would offer some assurance here. And I very much hope that the Department for Education moves quickly from its recent call for evidence to a concrete legislative solution."