The new building will be on the same scale as the huge structure of iron and glass designed by Joseph Paxton for the 1851 Great Exhibition in Hyde Park. It was the largest glass structure in the world before it was destroyed by fire in 1936.
It was later relocated to south-east London to the area which became known as Crystal Palace.
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The retrospective is so in-demand the museum will open its doors all through the night for the first time since it opened in 1857.