The Southbank Centre has unveiled plans to transform the complex around the Queen Elizabeth Hall, the Purcell Room and the Hayward Gallery.
The proposals include the refurbishment of the existing 1960s buildings and the creation of a new glass pavilion and a central foyer.
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David Cameron said the Met proved it can "do more with less" and declined to criticise the Mayor of London for his water cannon spend.
A group of disabled activists threw toys and balls at him as he entered the conference.
A wet start to the week and the unsettled weather is set to continue over the next few days.