A police officer can be seen in the live video feed from a camera worn by one of the climbers at the top of The Shard. It is not clear whether any of the protesters have been arrested.
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Rain will spread southeastwards through N. Ireland, Wales and England overnight.
The woman used her daughter's own Facebook page to live-stream the attack after the teenager posted provocative pictures online.
A senior employee at the organisation reportedly derided the three-year-old royal for being 'royal, rich' and "advantaged'.