The estimated final cost of the school project has risen from around £25m to £30.8m.
The all-girls Parliament Hill will see several of its old buildings demolished to make way for a large, curved contemporary teaching block and a new building in front of the existing main building.
Designed by architect Astudio, the Ribbon Building, as it will be known, will be clad in copper and has been designed to achieve the Passivhaus standard.
As well as teaching rooms, the proposed block will house a sixth-form centre.
The William Ellis boys’ school will be extended with a new two-storey addition clad in rich brown brindle brickwork which references the red-brown brick already used at the facility.
Works are due to start on site in April 2016, with a phased completion expected between Summer 2017 and Summer 2018.