Councillors are to ask the Department of National Heritage to withdraw the licence of the square's official food-vendor, in a bid to reduce the size of the flock.
Bernard Rayner, who owns the business, plans to fight the move. "I have been working here all my life. My family has been running this stand since 1952, and now they are trying to destroy my livelihood," he said. "Everyone loves the birds, especially the kids."
People of all nationalities flock to the square marvel at and feed the feathered gathering, and for many tourists it is as much an attraction as Buckingham Palace and Madame Tussaud's.
Two visitors from the United States, David and Carol Whisman, said that when they thought of England, they remembered Mary Poppins feeding the pigeons. "It is like an event in itself coming here, and it would be very disappointing if they got rid of all the birds," said Mr Whisman, 38. "There is only one place you can really come to feed them - and that's here."
But entertainment value is not the only thing the pigeons bring to the area. Every year, over a ton of droppings have to be removed from Nelson's column alone, and according to the council, it damages surrounding buildings.
A spokeswoman for the Department of National Heritage said there would be no immediate action as Mr Bernard still had two years left on his licence.
"We will consider what the council have to say. But Trafalgar Square is a recognised landmark and pigeons are part of the attraction," she said.
The pigeons, however, who declined to comment, seemed unruffled by all the fuss.