About 80 firefighters are dealing with the fire in Transport Avenue in Brentford.
It started at 12:08 GMT.
BBC London Travel reports there are delays on the M4 eastbound from Heston Services to junction 2 at Brentford. The smoke can be seen from Heathrow Airport about six miles (10km) away.
Fire crews are also dealing with a large at an industrial unit in north London.
About 70 firefighters are tackling the fire in Bernard Road, Tottenham, near Seven Sisters Overground Station.
They were called at about 10:00 GMT to a fire in a range of single storey units, the largest of which measures 30m (90ft) by 10m (32ft).
London Fire Brigade said it did not know the cause of the fire but half of the ground floor and roof had been badly damaged.
A large fire has started at a recycling centre in west London, with thick smoke billowing across the M4, causing delays.