The corporation's planning and transport committee voted to proceed with court action to remove tents from the public highways by the cathedral.
It came as the cathedral doors reopened after being closed for a week.
The Occupy London Stock Exchange protesters said the corporation wanted a "long, costly legal battle".
Members of the group set up their tents on 15 October and there are now more than 200 erected around the cathedral.
The cathedral closed its doors to the public over health and safety fears about the camp.