Lea junior school, in Slough, had timetabled four hours' private lessons during the school day in information technology every week with Ryde College, near Watford.
The parents of 16 pupils, all aged nine and 10, were asked to pay half the pound;1,200 fees of the course, which was due to begin in September. The college described the arrangement as unprecedented.
However, the school and college were re-thinking the move as The TES went to press after the local education authority said it went against council policy.
In a statement, Slough Borough Council said: "It is not our policy to charge pupils for lessons held in school time. Schools can make their own arrangements for extra-curricular activities."
Eamonn O'Kane, general secretary of the National Association of Schoolmasters Union of Women Teachers, said: "If such courses become more widespread they could threaten one of the great bulwarks of the state education service - education for all."
Mike Ryde, managing director of Ryde College, which has a tradition of putting very young pupils through GCSEs, admitted that the scheme went against the principle that parents should not be charged for courses in school time.
Raminder Vig, the school's outgoing head who brought in the college, said the scheme was voluntary and pupils not taking part would continue to receive their normal lessons: "Next year, we hoped to raise money to allow everyone in the school to benefit. If we have to, we will run it after school."
A Department for Education and Skills spokesman would not say whether charging parents for lessons during school hours was against the law. But official guidance issued to governors states that all education offered during school hours has to be free and that pupils should not be excluded from curriculum activities due to a parental inability to pay.