A mother and two children aged 11 and six were hit by a Ford Transit panel van.
Said Faiz Al-Hadhrami, 25, appeared before city magistrates on Monday over the incident in Fulbridge Road.
The prosecution says that he turned left at a roundabout and knocked down the pedestrians who were all already in the road.
Prosecutor Graham Allen said: “The actual allegation is that he has not applied due care and attention.”
Al-Hadhrami, who was not represented in court, admitted that he was the driver of the company van but denied the charge.
The case was adjourned for trial on February 15 and the defendant, of Crabtree, was granted unconditional bail.