A large blue rooster currently stands on the fourth plinth at Trafalgar Square, which has become a showcase for temporary artworks.
Mayor of London Boris Johnson said: "The placing of challenging artwork amidst the historic surroundings of Trafalgar Square creates a delicious juxtaposition that gets people talking and debating, underpinning London's reputation as a great world city for culture."
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The planning application said the museum would be dedicated to celebrating the achievements of East End women. Residents are very angry.