There has been a 65% increase in children recorded as home educated in the UK over six years.
Parents gave reasons including their lifestyle, dissatisfaction or disagreements with local schools, special needs, bullying and religion.
Responses to Freedom of Information requests from 190 local authorities showed 36,609 home educated children.
The government says it will continue to "respect the rights of parents to home educate their children".
There is no legal obligation for parents to send their children to school, although they have to provide a "suitable education" at home.
The figures show an increase of at least 10,399 pupils, up to almost 37,000, in a school population of about 9.5 million pupils.
The home-educated figure may be an under-estimate. When parents withdraw a child from school they are recorded as being home educated, but children who never start school may not be reflected in the statistics.
Among 190 councils with figures for 2014-15, there were 178 with data for the past three years, showing a 26% increase.
For 133 of the local authorities, there was data from 2009-10 to 2014-15, showing that numbers had risen by almost two thirds.
Graham Stuart, chair of the All-Party Parliamentary Group on Home Education, says it is possible councils have become better at recording information, and any figures are almost certainly an under-estimate.
"Local authorities have created groups to share best practice, and we're seeing what I hope is an increasing trend to stop treating home education as a problem to be regulated, and instead see it as an opportunity to be facilitated and supported," said the Conservative MP and former chairman of the education select committee.
Parents do not have to give a reason for withdrawing a child from school, but in 41 council areas there is information about the purpose, giving an insight into the variations among home-educating families.
Top of the list is a difference of philosophy or lifestyle at 13.4%. But this can be higher in some areas, for example in Gloucestershire this accounts for 235 of the 641 children being home educated.
This is followed by a dissatisfaction with the local school or a conflict, accounting for 9.3% of families. In Hertfordshire 240 out of a total of 724 parents gave this as their motivation.
Cultural or religious reasons are cited in 6.2% of cases, with bullying at 4.8% and special needs or medical problems at 4.3%.
With growing pressure on school places due to rising pupil numbers, 3.4% of home-educating parents say they could not get their child into a preferred school.
Dr Helen Lees, of Newman University Birmingham, has written extensively about alternative education. She believes some parents do not like the structured assessment and testing in schools.
She says parents find online accounts of the success of home education and are saying: "If they can do it why can't we do it. They're hearing from groups on Facebook or Yahoo that it's working well, the children are happy."
The recording of parents' motivations is patchy, partly because parents do not have to explain themselves, so there is no comprehensive information.
The same is true of the limited data about the families themselves.
In the very small number of local authorities where there is information on religion, about 31% of home educators belong to a faith group, although that may not be the reason they have chosen an alternative to school. Of those, half are listed as Christian and a third as Muslim.
The areas with the highest growth in home education are very different, suggesting there are many factors behind the increase.
In two counties where there are grammar schools, numbers have remained relatively high, reaching 1,429 in Kent and 1,191 in Essex.
And in Rhondda Cynon Taf where there were five home educated children recorded in 2009-10 there are now 65.
There has been concern expressed recently by Ofsted that a very small number of people may be misusing the right to home educate to place their children in unregistered, and potentially illegal schools.
That concern has been echoed by the Education Secretary Nicky Morgan who has asked the Chief Inspector of Schools Sir Michael Wilshaw to collect evidence for potential prosecutions.
The government is consulting on greater regulation of part-time education settings providing more than six to eight hours a week of tuition.
It has made clear in the consultation that it does not wish to interfere with the legal right of parents to choose how their children are educated.
"The government continues to respect the rights of parents to home educate their children, whether at home or in a combination of other settings, provided a suitable full-time education is being arranged."