The shop targeted in Sloane Square is Gucci's flagship store.
It's thought that the Mercedes used to reverse into the glass doors may have been stolen.
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West Ham have opened an investigation into a flyer that was allegedly distributed ahead of the game with Chelsea.
Damon Joseph Smith smiled and waved at his mother, who waved back.
Tanguy Marie De Carne, 53, jumped red traffic lights and rode on busy pavements through the City pursued by police