Instead, the primary pupils are being encouraged to play in large groups.
Educational psychologist Gaynor Sbuttoni said the policy has been used at schools in Kingston, South West London, and Surrey.
She added: "I have noticed that teachers tell children they shouldn't have a best friend and that everyone should play together.
"They are doing it because they want to save the child the pain of splitting up from their best friend. But it is natural for some children to want a best friend. If they break up, they have to feel the pain because they're learning to deal with it."
Russell Hobby, of the National Association of Head Teachers, confirmed some schools were adopting best-friend bans.
He said: "I don't think it is widespread but it is clearly happening. It seems bizarre.
"I don't see how you can stop people from forming close friendships. We make and lose friends throughout our lives." The Campaign for Real Education, which wants more parental choice in state education, said the "ridiculous" policy was robbing children of their childhood.
Spokesman Chris McGovern added: "Children take things very seriously and if you tell them they can't have a best friend it can be seriously damaging to them. They need to learn about relationships."
