When officers pulled him over they got the impression Churchill had been drinking.
The 25-year-old failed a roadside breath test and was taken to a police station, where he gave a reading of 69 microgrammes of alcohol per 100ml of breath.
The legal limit is 35 microgrammes.
Sheital Maher, representing Churchill, a Formula 1 sports analyst, at Leicester Magistrates' Court, said: "He is remorseful. He was in Leicester, having consumed alcohol with a friend in the city centre.
"He was travelling in the wrong direction, not being familiar with the area. ...