The local Greek community says the school is needed because second and third-generation children, many from mixed marriages, are losing touch with their heritage despite the existence of Saturday classes.
"The religion is our primary focus," said George Kastelanides, of the Greek Association for Language Enhancement, which will run the school. "Our language and culture stems from that. Many of our children born here don't speak Greek. If they don't speak the language they can't understand the religion.
"They are born here and are British citizens, but they also have their heritage which they need to have defined and taught in order to become fully-rounded, strong people."
Around 450 families have pre-registered for St Cyprian's, named after a Greek saint. Education Secretary David Blunkett is said to be "favourably disposed" provided the remaining difficulties are ironed out.