Wendi Deng is perhaps best known in Britain for defending husband Rupert during a physical attack at a parliamentary hearing in 2011.
The Chinese-born businesswoman was seen landing a slap on the face of activist Johnnie Marbles, who had attempted to throw a foam pie at Mr Murdoch.
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Michael Fallon has received reassurances from his US counterpart that security ties with Britain will "endure" following a vote for Brexit.
On Friday, police said it appeared the girl had shot herself in the face with the weapon.
The showers will be slow-moving, heavy and thundery at times, particularly in central and eastern areas.