The fire service said they received reports of the blaze on New Zealand Way in White City, at 6.52pm on Saturday evening.
Three men were rescued from the single storey building by firefighters and treated at the scene by paramedics.
Of these, two were declared dead and another died later in hospital after being taken there for further treatment, the LFB said.
Speaking from the scene, LFB assistant commissioner Pat Goulbourne said: “The fire involved a single storey pavilion, with just over half of the structure damaged by the fire.”
He added: “Control officers mobilised crews from North Kensington, Acton, Chiswick and surrounding fire stations to the scene.
“Firefighters were able to bring the fire under control by 9.25pm.
“The cause of the fire is under investigation by the Brigade’s specialist fire investigation officers and the Metropolitan Police Service. “

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