A ban on in-school coaching for the 11+ exam should be reviewed, the leader of Kent County Council has said.
In-school coaching is not allowed by the council, to level the playing field for grammar school access across independent and state primaries.
But an undercover BBC reporter visited 10 fee-paying primary schools in Kent and found nine were tutoring pupils.
Council leader Paul Carter said: "Why shouldn't local schools, as well as private schools, be able to coach?"
A BBC South East reporter posing as a parent found the private schools were running extra classes and summer schools focusing on the exam.
Also referred to locally as the Kent Test or Medway Test, it consists of English, maths and reasoning. This year's exam is being held on Thursday, 6 September.
The best performers will be offered places at grammar schools, which generally outperform their non-selective counterparts.
However, critics say children from wealthier backgrounds have an unfair advantage because they are often coached in school, or have private tutors.
Mr Carter told the BBC a review was needed.
He said: "All schools should be helping and supporting those that have got the ability to get into grammar school, to help, support and prepare them for the 11+."
Asked if it was time to get rid of the ban on coaching within schools, he said: "That's my view. Why shouldn't local schools, alongside the private schools, be able to coach their children to pass the 11+?"
Labour's shadow schools minister Mike Kane MP said: "The selective education system in England is not working effectively. It doesn't select by ability, it selects by income, the socio-economic status of a family."
In a series of recordings with private schools teachers, who cannot be identified for legal reasons, one said: "It's ridiculous they say you can't be tutored for it... we prepare children for the Kent Test - 100%."
Others were open about giving children examples of past papers, and mock tests "structured in a very similar way" to the Kent Test.
Only one head denied any extra tutorials, saying "no school should be coaching children".
Kent County Council administers the test. It does not specifically define coaching, but said using previous papers for children to practise the question styles would break the rules.
Councillor Roger Gough, cabinet member for children, young people and education, said: "It should be apparent this is not an appropriate approach to a process which seeks to identify the most suitable type of educational placement for children leaving primary school by assessing their ability."
The county council said it would "always look at any firm evidence that suggests a school may have engaged in coaching" and schools found in breach of the rules could be banned from holding future exams.
Three were warned about coaching by the council in 2016, but no further action was taken and the council has never banned a school from holding the exam.
Angela Culley, from the Independent Schools Association, said she disagreed with stigmatising private school coaching, when families also had the option to hire private tutors.
She said: "Out there we have tutoring centres preparing children for the 11+ exam. What's the difference?"
For more on this story see BBC South East's Inside Out on BBC One at 19:30 BST on Monday 3 September.