Eyewitnesses have been posting photos of massive black clouds billowing from near the airport buildings. Some of them have reported hearing "clearly the sounds of explosions" at the blaze which is close to the railway line.
Commenting on the situation, National Rail has informed the general public that train services may be "delayed or cancelled until approximately 4.45pm".
Fire crews and police have been deployed to the scene, while the roads around the area have been closed.
"Six fire engines and around 40 firefighters have been called to a fire at a warehouse in Wimpole Road in West Drayton. A container storage yard is alight. The fire is very visible and is producing a lot of smoke. Residents and businesses in the area should keep their windows and doors shut," a spokesman for London Fire Bridge said.
No information on possible casualties or damage as well as on a possible cause of the fire has been provided yet.