Bovey was singled out as a favourite during the early stages of the show, but White axed the property developer because he claimed that it wasn't possible for him to have two leaders in the kitchen.
"In service, you preferred to sink than ask for help," said White. "You are not a team player - that's what you've proven to me tonight. You are a leader, you're a boss.
"That kitchen is not big enough for two bosses. I am the boss of Hell's Kitchen."
Bovey claimed that the reality TV experience had been a positive one for his relationship with Anthea Turner and backed her to go on and win the show.
"Being on the show together has made our relationship stronger and we can finally cook together without bickering," he told The Sun. "Though I think she'll force me to do a lot more at home now!"
On Sunday, Shameless star Jody Latham became the first contestant to be axed from the series after a string of rows with Bovey, Turner and comic Adrian Edmondson.
Speaking about Latham, Bovey said: "I was offended by his bust-up with Anthea because he'd offended my wife. I think in the heat of the moment he forgot where he was."
Edmondson and ex-Liverpool footballer Bruce Grobbelaar are the bookmakers' favourites to win the ITV1 show.