"It is well known that families pay their way into this school," one parent, who did not want to be named, said.

They said some families were asked to pay an extra $1000 to $2000 on top of this, "particularly if they have a Dr in front of their name".

But co-principal Megan Smith said the payment was the school's normal fees, and not an extra charge.

She said the school had asked families living outside its area to pre-pay school fees to ensure they would attend. This practice was stopped in late 2015 following advice from the Education Department and a review of the school fee schedule, she said.

"The suggestion that Clifton Hill Primary School has accepted enrolments based on offers of payments in excess of scheduled fees is outrageous and untrue," she said.