The world-famous revolving sign will be retained at the new building, as well as the Eternal Flame and Roll of Honour, which are currently located at New Scotland Yard in Victoria.
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Scotland Yard recorded 1,235 Islamophobic attacks in the last 12 months, compared with 811 in 2015.
Officers say the child, aged two, was targeted in the Lewisham Shopping Centre.
New figures show London Fire Brigade received 6,820 malicious hoax calls last year, almost twenty a day.