A five-year-old girl injured when a car crashed into a tree, killing her father at the wheel, may have been in the wreckage for some time before she was discovered, the ambulance service has said.

Police are appealing for witnesses after emergency crews found the girl in the back of the black Ford Fiesta. The vehicle was discovered in a ditch in foggy conditions on Sunday morning by two cyclists, who alerted authorities.

The child’s 25-year-old father, who was driving the car, was found dead at the scene on the B5030 at Crakemarsh, Uttoxeter. Police said he was from the area.

West Midlands ambulance service said the car had “suffered considerable damage” and appeared to have been there for some time.

“It was very foggy at the time. Unfortunately, it was immediately obvious that the man driving had passed away. This was an extremely difficult incident for all involved including the two cyclists who made the discovery,” a spokesman said.

Neither the man nor his daughter have been named as police said they were yet to be formally identified, and officers are working with family members to establish the likely time of the crash. It is understood the driver was seen alive on Saturday evening.

The girl was taken to Royal Stoke University hospital after complaining of pain in her back and abdomen, but Staffordshire police said her injuries were minor.David Scawthorn, a kennel owner from Crakemarsh who lives close to the scene of the incident, said the mist had begun to descend late Sunday afternoon. “I heard there had been a crash on the radio this morning, it is horribly sad. It’s a quiet road at night, with not many people travelling on it. Brook Lane, a country lane next to that road has some potholes which are up to seven inches deep. But the B5030 is a good road, built quite recently,” he said.

“One of the girls who works at the kennels came from Stoke this morning and she said it had been very foggy on her way in. But fog always happens this time of year around here.”

A police spokesman said officers were keen to speak to anyone who might have seen the black Fiesta before the collision.

“Specially trained family liaison officers are working to support the family at this difficult time,” a police spokesman said. “At this early stage of the investigation it is not known what time the collision occurred. Anyone with information is urged to call Staffordshire police on 101 quoting incident 300 of 1 November.”

The Met Office has issued a weather warning for the area and much of the rest of the England due to the dense fog, which formed on Sunday night. It said travel might be impacted by poor visibility. Visibility had been less than 100 metres at times, forecasters said, but the fog was expected to lift slowly and clear throughout Monday.