Finalists Richard and Adam Johnson were performing on Saturday night's show when backup singer Natalie Holt, 30, egged the judges, ITV News reported.
The Johnson brothers kept singing and Holt was pulled off stage, BBC Radio 1 reported.
Producers issued a statement saying they called police "as a result of [Holt's] misguided actions."
"However, we have decided to take no further action at this stage," the statement said.
"I want to apologize to Richard and Adam for overshadowing their performance," Holt said in a statement released by the show. "I've never done anything like this before and in hindsight I have realized it was a silly thing to do."
The Hungarian dance troupe Attraction went on to win the competition, earning more than $32,000 and a chance to perform at Royal Variety Performance.
"It just shows that this country welcomes people from all over the world and they loved this act," Cowell said of Attraction's win.
"I really don't like eggs now," he said.