The extra troops, who were already standing by on 48 hours’ notice, bring the total military deployment at the 2012 Olympics to 18,200.
The decision was taken at a cabinet committee meeting chaired by Prime Minister David Cameron, with just three days left before the Games officially open.
While the numbers of security staff being provided by the beleaguered G4S continues to rise, ministers wanted to “leave nothing to chance”, Hunt said.
“Security staffing levels at venues have been kept under constant review,” Hunt said.
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