Police are aware of the damage to the auto, a London Ambulance Service spokesman confirmed.
Police have now confirmed that one of the people - a woman - has been identified.
Emergency services urged people to share photos on social media to help them find people who damaged the vehicle.
Meanwhile, West Midlands Police said they took their highest volume of 999 calls ever, with 3,276 being made for emergency police assistance in 24 hours.
In Nottingham, a group of supporters were seen dancing on top of a bus shelter, while other clips from Manchester and Birmingham showed people on top of buses with their shirts off.
The auto was left with a completely smashed windscreen and heavy denting to the bonnet, roof and bumper.
"We are aware of a small group of fans celebrating the match result in one of our stores", a spokeswoman said.
England manager Gareth Southgate says winning the World Cup would make his players even bigger heroes than the 1966 generation because of the impact of social media and the globalisation of football.
England has to win two more games to bring the World Cup home, but the enthusiasm some soccer fans displayed after their team advanced to the semi-finals met worldwide expectations.
"And we have to be like that, I think, if we are going to get in the final, so we'll have to perform well and play well."
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