Lincolnshire Police said at the time that the cars were being driven at high speed in front of a large crowd when they crashed on Whisby Road in Lincoln in August 2021.
Bailey Davis, 20, of Chestnut Street, Ruskington, denied a charge of dangerous driving when he appeared at Lincoln Crown Court on Thursday, but admitted careless driving.
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Robert Haines, 33, of Reedbush Avenue, Cherry Willingham, previously admitted four counts of dangerous driving.
Recorder Simon King adjourned the case for a further mention hearing at Lincoln Crown Court on November 14.