Crowds are beginning to gather in Tahrir Square to protest against President Mursi's new powers. State television showed a number of protests outside mosques across the city.
Supporters of the president have been staging counter protests, but there are no reports of clashes.
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The BFI made the move in the wake of the sexual harassment allegations made against him by a large number of women in the film industry.
A mild day for most with plenty of misty low cloud.
Hollywood star Channing Tatum broke the news in a lengthy Facebook post as he paid tribute to Harvey Weinstein's accusers.