The show was disrupted by a member of the backing orchestra hurling eggs at the judges, one of which hit Simon Cowell on the jacket.
A spokesperson said: "During tonight's show an incident took place during the finale of Richard and Adam's performance.
"Natalie Holt (age 30) was part of the backing group for their performance and as a result of her misguided actions the police were called. However, we have decided to take no further action at this stage."