About 15 fire engines and 97 firefighters were deployed to tackle the fire in Feltham which started at about 4pm on Saturday.
The blaze was brought under control at around 9.45pm.
A London Fire Brigade spokeswoman blamed the fire on the current long stretch of dry weather.
She added that such fires were “very unpredictable”.
There were no reported injuries, although 14 horses were moved from a nearby field to a safer place.
The smoke travelled as far as Heathrow but a spokesman for the airport said the fire had “no impact” on its operations.
Both runways continued operating normally, with no delays due to the incident, they added.