Bradford, Birmingham and Luton councils are doing too little to trace pupils who go missing from mainstream schools, says Ofsted chief Sir Michael Wilshaw.
Sir Michael says children educated at home, in unregistered schools or in some independent faith schools can be at risk of exposure to extremist views.
The government said it was taking tough action on unregistered schools.
The three councils said the comments were a surprise but they were committed to improving safeguarding practices.
Sir Michael raised his concerns in a letter to Education Secretary Nicky Morgan.
In it he says the three councils are failing to keep proper track of missing pupils removed from their schools in the middle of the year.
This, he says, leaves children vulnerable to "harm, exploitation or the risk of falling under the influence of extremist views".
Sir Michael highlights continuing concerns about the performance of Birmingham City Council "and its ability to provide the necessary help and protection for children in need, as well as to ensure the safety of all school-age children in the city".
He says services to help and protect the city's vulnerable children remain "very poor" while the safeguarding of children in schools "is weak and lacks sufficient rigour".
And, according to the letter, the council is failing to trace children missing from education.
Some are simply removed from the council's records, with 253 missing children taken off the list without being located between September 2015 and January 2016 alone, Sir Michael notes.
Two years after the Trojan Horse allegations about a group of conservative Muslims taking over a number of Birmingham schools, Sir Michael says "the situation remains fragile".
Many of the schools have improved and children are much safer, while Ofsted continues to monitor progress and he himself makes frequent visits to the city, he writes.
But recent meetings with head teachers have revealed "a minority of people in the community who are still intent on destabilising these schools".
In one meeting, a group of heads spoke of feeling "isolated and vulnerable" without co-ordinated support, says the letter.
Some complained of a continuing "culture of fear" with "overt intimidation from some elements within the local community".
The heads highlighted:
- organised resistance to personal, social and health education (PSHE), which includes sex education and the promotion of equality
- derogatory comments posted on social media
- continual pressure from some parents to change schools' curriculum and staffing
"A number of heads said that they felt unsupported by the local authority in confronting these challenges," the letter continues.
Sir Michael recommends the three councils be monitored on a termly basis by dedicated Ofsted inspectors, reporting directly to him and to the education secretary.
A Department for Education spokeswoman said the government had announced a significant escalation of Ofsted investigations into unregistered schools and has "a team of inspectors dedicated to identifying, investigating and prosecuting such settings.
"We are working with the Crown Prosecution Service to take tough action on this issue."
The government is also toughening up requirements for schools to inform councils about pupils who are removed, said the spokeswoman.
"Ofsted acknowledges that schools have improved and we should praise the professionals involved.
"However, we must remain vigilant against a small minority in communities who seek to undermine fundamental British values," she added.
Brigid Jones, Birmingham's cabinet member for children, families and schools, said the council was fully committed to delivering improvements and a recent inspection had confirmed they were progressing according to plan.
"We found the comments in Sir Michael's letter to be a surprise.
"In terms of the chief inspector's comments on schools in Birmingham, we note what is being said but contend they don't fully reflect the feedback that we receive from teachers, our education commissioner and the positive views of other government departments on our work on extremism."
Susan Hinchcliffe, leader of Bradford Council said nothing was more important "than keeping our children safe".
"Since the initial meeting with Sir Michael, we have already taken action across the areas identified to tighten our processes and have invited open scrutiny of our practice in this area."
Luton's chief executive, Trevor Holden, called the letter "both inaccurate and ill-advised" and in contradiction to Ofsted's most recent inspection report, which made no recommendations about safeguarding or children missing from school or in home education in the borough.
"As a council we are committed to working closely with Ofsted to improve educational services and safeguarding practices for the children and young people of Luton," said Mr Holden
"I have contacted the chief inspector to clarify his concerns."