A change in the law is needed to force parents to declare when their children are being home-educated, councils say.
Currently, parents do not need to tell their local authority when a child is being taught at home, unless they have been removed from school.
Portsmouth and Reading are among the councils who want a register after the number of home-taught children in the UK rose by 65%, between 2009-15.
Parents say the state should not dictate what is best for children.
Portsmouth City Council’s education cabinet member, Councillor Neill Young, said: “I think it’s important that we get a registration scheme so that we can monitor these young people being home educated.
“But also we have to think about the safeguarding of these young people.
“People who don’t want the local authorities to know what they are doing would be a cause for concern on a number of different levels.”
‘Sociable, happy children’
Reading Borough Council agreed there should be a “mandatory requirement to register children”.
Kathryn Smutek, who educates her five children at home in Portland, Dorset, admitted they are “not monitored”, but “we wouldn’t be hard to find if they wanted to find us”.
“They are learning all of the time… I don’t want to prove it and, legally, I don’t have to, but they are sociable children, they’re happy children,” she said.
“People need to be free to educate and to live the way that they see fit, within the bounds of the law.”
Sam Martell, from Wheatley near Oxford, said that home-educating her four children was simply “an extension of parenting” and no register was needed.
She said: “It’s insulting to think that people who have chosen this way of life may be harming their children.”
A Local Government Association spokesman said the majority of home educators worked with councils to provide a good education.
“[But] in the small number of cases where there are concerns for children being home-educated, gaining access to properties is extremely difficult, and councils need more powers to ensure children’s safety,” he added.
The Department for Education said home education needed to be “of suitable quality”.
A spokesman said: “We are taking steps to ensure the system is as robust as it can be when it comes to protecting young people, while at the same time safeguarding the rights of parents to determine how and where to educate their children.”