A woman - later identified as 30-year-old Natalie Holt, a member of the backing orchestra - invaded the stage during Richard and Adam's performance of 'The Impossible Dream' and began throwing eggs in the direction of Cowell and the other judges.
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She ran forward when the backing singers were revealed by the opening screens at the rear of the stage, making her way past the singers with a box of eggs in her hand.
Security quickly escorted Holt off the stage but only after she had successfully hit Cowell on his jacket.
A spokesperson for BGT 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."
Holt competed on the show herself in 2012 as part of Raven Quartet, and her professional achievements include working on the BAFTA-nominated score for the BBC's 2011 Great Expectations adaptation.
The viola player said in a statement: "I want to apologise to Richard and Adam for overshadowing their performance. I've never done anything like this before and in hindsight I have realised it was a silly thing to do."
After the performance, Cowell said: "I sent a tweet out saying I don't like eggs and I really don't like eggs now."
Richard and Adam laughed off the incident, saying that their infamous nan would be "going after her", and later added in a statement that they are "proud" to have made it to the end of the song.
Watch the egg-throwing incident (beginning at 1.48) below: