The incident occurred on Wednesday after Mr Mitchell, MP for Sutton Coldfield, was told by officers to get off his bicycle as he left Downing Street and use the smaller pedestriangate instead of the main entrance used by cars.
He was alleged to have used the word during an altercation with police from the Diplomatic Protection Group (DPG) outside Downing Street in September, when they asked him to use the pedestriangate rather than the maingate.
His outburst came after armed police stopped him from cycling through the main Downing Street gate, instead directing him to the smaller pedestriangate.