The incident at Malins Gate, Great Linford, Milton Keynes, took place at 12.34am, with one appliance and crew from Broughton attending.
Firefighters used one set of breathing apparatus and one hose reel jet. The car was 50 per cent damaged by fire.
Later fire crews were called after a large pile of woodchips caught light in Paddocks Lane, Woburn Sands.
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One appliance and crew from West Ashland and one from Broughton attended shortly after 7.30am.
Firefighters using two hose reel jets with fog spike attachment, small gear and thermal imaging camera bring the blaze under control.
They also attended an incident in Osborne Street, Bletchley after an engine oil spill on to the road.
One appliance and crew from West Ashland attended.
The incident was referred to the local Highways team due to the quantity of oil on the road.