Yasmin Smith, who rushed to Bradley Wiggins' aid, has told Daybreak that the woman involved in the collision didn't realise who he was at first.
"She was even more upset when the police told her who she had hit," she said.
Team Sky, who Bradley Wiggins rides for, has said the Tour de France winner is expected to "make a full and speedy recovery":
We can confirm that on Wednesday evening Bradley Wiggins was involved in a road traffic accident whilst riding his bike near his home in Lancashire.
He is being kept in hospital overnight for observation but the injuries he has sustained are not thought to be serious and he is expected to make a full and speedy recovery.
We will announce more details in due course.
The accident happened at about 6pm in Wrightington, Lancashire, which is near to Bradley Wiggins' family home in Eccleston.
The driver of the Astra, a local woman, was uninjured.
A police source has told the Press Association that Bradley Wiggins' injuries from the crash were thought to be very serious at first, but later it appeared he suffered a number of broken ribs and cuts and bruises:
– Lancashire Police
Police were called to the scene of a road traffic accident at Crow Orchard Road in Wrightington at about 6pm this evening.
A cyclist has been involved in a collision with a white Vauxhall Astra car.
The rider of the bike, a 32-year-old local man, was taken to hospital by ambulance with injuries not thought to be life-threatening.
His family have been told.
Team Sky has said that Bradley Wiggins sustained "minor injuries" in the collision, Sky News reports.
Bradley Wiggins' crash came days after the Tour de France winner had shaved off his "lucky" sideburns.
They were too recognisable — it was getting a bit much. Now I can put a hat on and no one knows who I am.
Bradley Wiggins has been outspoken about cyclists' safety on the roads in the past.
Cyclist Bradley Wiggins is thought to have been involved in a collision outside the BP petrol forecourt seen below, according to local media reports.
He was reportedly travelling down Crow Orchard Road near the junction with Mossy Lea Road, around 100 metres from the M6 north of Wigan, Greater Manchester.