According to him, the intensity of training under Jose Mourinho was so high that the Portuguese manager contemplated having his players wear shin pads when Essien joined.
The Ghanaian made a big-money move to Stamford Bridge in 2005 to play under the tutelage of Mourinho.
The Blues spent £24.4 million to prise Essien away from Lyon, making him the club’s record signing at the time.
The 38-year went on to enjoy massive success at Chelsea, winning multiple titles, including the Premier League and the Champions League.
"The tempo was completely different when I moved to Chelsea. There was a real step up in quality as well,” Wright-Phillips told Bonus Finder.
"It only got worse when Michael Essien joined because Mourinho was at the point where he was thinking about getting the players to train with shin pads on.
“There was so many tackles flying in and training was really competitive so I don't think we would have blamed him if Mourinho made that decision.”
Wright-Phillips was, however, quick to add that the seriousness of the players under Mourinho made the team successful.
"To get the chance to play with players like that and win trophies with that team was a dream come true for me. It helped me to improve as a player.
"It was a period that was an amazing time. The fans were superb, Roman Abramovich was amazing and Mourinho... I thought he was a fantastic manager and a great man in general," he added.
Essien is currently an assistant coach of Danish topflight side Nordsjaelland, having hanged his boots from professional football.