The number of children being homeschooled has risen by about 40% over three years, the BBC has found.
Across the UK 48,000 children were being home-educated in 2016-17, up from about 34,000 in 2014-15.
Mental health issues and avoiding exclusion are two reasons parents gave for removing children from classrooms.
The government will publish new guidance on the "rights and responsibilities on home education" but councils want more monitoring powers.
They are concerned about the quality of the education homeschooled children receive as well as "safeguarding" issues, such as the ability to properly protect children from abuse or maltreatment.
Dr Carrie Herbert, the founder of a charity for children outside mainstream education, said the rise in homeschooling suggested "something quite tragic about the state of the education system".
She said she was concerned some parents might also feel pressured into home-schooling their children to avoid exclusion or prosecution over poor attendance.
"I'm not sure it's very useful anymore to put 30 children in one classroom with an adult all doing the same thing in the same way at the same time," said Dr Herbert, of The Red Balloon charity.
"We should really be thinking more 21st century and outside the box about this and teaching online in real time can help do this."
'My son was treated as a problem'
Oliver Wood, from Thetford in Norfolk, was severely bullied at his former school before becoming a pupil of Red Balloon.
The 15-year-old has autism and suffers from anxiety.
"Every school we were offered was looking at him like a problem to solve, rather than a person they could work with," said his mother, Sophie.
Oliver hopes to take four GCSEs next June.
Red Balloon has an online school that follows a "normal" school day as much as possible.
Its curriculum is tailored to suit the child's interests, with the aim of getting them back into the habit of learning, socialising with others and for some, returning to school.
The charity has 93 pupils and has had to close its books until it can afford to hire more teachers.
The BBC contacted councils in England, Wales and Scotland and the Northern Ireland Department of Education for figures on homeschooling.
Of the 177 authorities that were able to provide data for all three years, 164 reported an increase.
Only 11 with figures for all three years had fewer homeschooled children in 2016-17 than in 2014-15.
While they make up just 0.5% of the school age population for England and Wales, the large rise has prompted calls from councils and education bodies for more statutory monitoring powers of homeschooled children.
You may also be interested in:
There is no legal obligation for children to attend school but the law says they must receive an education.
They can be taught by parents or private tutors and the guidance from both the English and Welsh education departments is that it must be a "suitable education".
The Association of Directors of Children's Services (ADCS) in England wants parents and carers who home-educate to be obliged to register with their local authority and for inspectors to be able to take action if they find a problem.
Councils should have resources to ensure homeschooled children receive "a good standard of education, delivered in a suitable learning environment and that they are safe," the ADCS said in a report in December 2017.
Safety of pupils was also raised in a study by Norfolk County Council.
Its children's services reported an "unprecedented year-on-year rise" in home-schooling with 1,309 (1.1%) of its school-aged pupils being home taught during the 2016-17 academic year.
"Given that children by the nature of being home-educated can be essentially 'invisible', an inability to make timely and appropriate contact with these families has an inherent risk attached," they said.
The Isle of Wight has the highest proportion of home-educated pupils, almost one in 50.
Criticisms by Ofsted over the island's high proportion of "inadequate" schools may have had an impact, the council said, adding it was tackling "lower educational standards".
A spokeswoman said it had a "good relationship" with many families contacting it "directly when they are thinking of home-educating" as another possible explanation for the figures.
In Wales just over 1,800 out of about 430,000 children, about 0.4%, were homeschooled in 2016-17.
In Scotland, just 0.1% of children are home-educated, 969 in total.
The department of education in Northern Ireland saw just 293 pupils being home educated out of a possible 343,082, representing less than 0.1% of the school-aged population in 2017.
Why are parents choosing to educate children at home?
Many authorities could not provide reasons why more parents appeared to be choosing homeschooling. Of those that did, the reasons included:
- Devon: Most parents who offered a reason for homeschooling blamed "dissatisfaction with the school environment"
- East Sussex: Lack of school choice, unmet special educational needs and the "rigour and limits" of the current school curriculum
- Gateshead: Parents felt some pressure from school to remove their children especially if the young person had poor attendance
- Cambridgeshire: The council said it had increased support for the home-educated community, including extending "borrowing rights" at libraries
- Darlington: Local authority staff are "currently working with the police and health to ensure the safeguarding of home educated children and this may have contributed to the rise in numbers identified"
In December Ofsted's chief inspector, Amanda Spielman, found overseeing the growing number of home-educated children was "becoming a challenge for local authorities."
The education watchdog also observed the numbers of children with special educational needs or disabilities guided towards home-education "was typically high".
Ms Spielman said it was "unacceptable" that parents reported being asked to keep their children at home because school leaders said they could not meet their children's needs.
A bill seeking more powers for local authorities to assess children receiving home education has gone through a second reading in the House of Lords.
Speaking in parliament, education minister Lord Agnew said many parents home-educate for "positive reasons" and it should be allowed to continue "with a minimum of fuss and bureaucracy".
"There is a need to ensure that, where there is genuine cause for concern about a child, local authorities are clear about the powers open to them," he said.
The Department for Education (DfE), which covers England, and the Welsh government will both consult on ways to improve home-education guidance for parents and councils.
A spokesman for the DfE said this would ensure local authorities "are clear on the action they can take where these responsibilities are not being met".
A spokesman for the Welsh government said: "We recognise that we are currently unable to provide reliable figures on how many children are educated at home and that is one of the reasons why we will be consulting on a database as well as statutory guidance for elective home education."