According to Sky News, eighty firefighters and 12 fire engines were called in at around 10 pm and managed to douse out the blaze within four hours.
The blaze damaged the first and second floors of the flat.
A London Ambulance Service spokeswoman said, "We were called at 9.59pm yesterday (6 February) to Holland Park Gardens, W14, to reports of a fire. We sent an ambulance crew, our Hazardous Area Response Team, an incident response officer and London's Air Ambulance trauma team in a car to the scene."
"Sadly, despite extensive resuscitation efforts, one patient - a man - died at the scene," she added.
So far, no one has been reported injured. The cause of the fire is yet to be ascertained and an investigation is underway.
The Holland Park Gardens houses well-known personalities such as former England footballer David Beckham and his wife Victoria Beckham, singer Robbie Williams and popular reality television judge Simon Cowell.