Redknapp wrote in The Sun: "Malky Mackay, Steve Bruce and Ian Holloway fly the flag for Team GB as the managers who got their clubs promoted from the Championship.
"To get a team promoted is a hell of a task and I believe all three teams have a great chance of staying up next season.
"Mackay is a first-time top-flight manager and no doubt will be looking forward to the challenge.
"Holloway was a breath of fresh air the last time he was a Premier League boss.
"I watched his Blackpool side a lot as I was Spurs boss at the time and I was hugely impressed with his philosophy.
"As the play-off winners, Crystal Palace are probably classed as the weakest of the three promoted teams.
"But with his character and experience of managing a smaller club in the Premier League, he will do fine. He is the first to admit that his squad needs work done to it.
"Bruce has done an amazing job bringing Hull up because they were not on anyone’s radar.
"He has done it in the Premier League and he will know he needs to add experienced players."