Leading architect Sir Terry Farrell claimed a new runway would kick start an Olympic-style boost for the economy of South London.
Sir Terry has been commissioned to draw-up plans for expanding the airport as part of a new campaign called "Gatwick Obviously".
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The Labour mayor will seek a second term in City Hall.
The Apprentice boss tweeted a picture of the sports team, which had been edited to include a picture of handbags and sunglasses.
The 23-year-old, from Enfield, north London, has been released by police under investigation.