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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The 47-year-old man died shortly after 3pm on Tuesday.
Specialist explosive detection dogs searched through the town examining letter boxes and phone booths for signs of potential devices.
Temperatures reached 29.1C in St James's Park, central London.