Wakefield Council has written to the government to express concerns about its "limited powers" of involvement with home schooled children.
Members of the authority's children scrutiny committee have repeatedly raised concerns about a lack of regulation around the home schooling system
Parents are legally entitled to educate their child at home but local councils currently have no rights to make visits to those pupils, and check on whether their tutoring is adequate.
On Wednesday, the council’s children’s services director told the committee that the Department of Education had been contacted about the issue.
It came as the committee’s deputy chair asked about the health of youngsters who don't attend school.
Councillor Kathy Scott said: “One of my concerns is about children who are home schooled.
"I know that the majority of home schooled kids are really well looked after, but there might be the odd one that hasn’t been immunised, for example.
“What can we do about that?”
Children’s services director Beate Wagner responded: "When it comes to children who are home schooled, the council has very limited powers.
"We could probably do more. We have staff who do keep in touch with those families but there's a degree of choice over whether those families engage with us or not.
"I know we’ve had a discussion about this previously and we’ve written to the Secretary of State (for Education) about how little we can do."