Cracks are visible on some of the chimneys and need to be rebuilt for safety reasons and to ensure they last, say the developers.
But campaigners say taking the chimneys down will ruin the character of the building.
A small group of people dressed as monkeys gathered outside the station today with placards claiming the company behind the development 'don't give two monkeys' for the iconic building.
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The Marsh & Parsons poster - captioned "a charming period property with a modern extension" - soon prompted criticism.
The track will be demolished to make way for a housing development and a new Stadium for AFC Wimbledon.
Just four authorities (Hammersmith & Fulham, Hillingdon, Newham and the City of London) have chosen to freeze council tax altogether.