Crowds gathered in London following the win and a group of England fans began urging people to climb on the ambulance, that had been parked near Borough Market.
The pictures quickly went viral and now officers say they have identified the woman in one of the photos but no arrests have so far been made.
A Scotland Yard spokesman told Metro: ‘Enquiries remain ongoing and no arrests have been made. Detectives from Southwark are investigating and are aware of images circulating via social media.
‘Enquiries are underway to trace those involved.’
A man dressed in a Gareth Southgate waistcoat also celebrated on the roof of the vehicle before the police arrived to prevent any further damage.
The London Ambulance Service said the actions of the group put a ‘big dampener on the celebrations’.
They wrote: ‘We’re delighted with the result, but this has put a big dampener on the celebrations for us.
‘While our officer attended a call nearby, this car was damaged in Borough High Street during the celebrations after the game. It’s now off the road to be repaired.’
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Football fans have now been warned not to ‘overstep the line’ during England’s World Cup semi-final match tonight.
Police are gearing up for Wednesday’s clash against Croatia, hoping to avoid a repeat of the alcohol-fuelled scenes at the weekend.
Police forces across the country were inundated with 999 calls following England’s victory over Sweden on Saturday, with many receiving more than on New Year’s Eve, and West Midlands Police experiencing its busiest ever 24-hour period.
Chief Superintendent Graeme Openshaw, from Greater Manchester Police, said: ‘Fans have to strike a balance and we’d ask people not to overstep the line and be respectful of others around them.
‘Unfortunately, we are aware that people have been climbing on emergency services vehicles and blocking buses – not only is this dangerous but this is also stopping people from doing an important job.’
Nottinghamshire Police warned that as well as an increased presence in the city on Wednesday, a number of other tactics were under discussion including officers potentially applying for banning orders for fans who cause trouble while watching a public showing of the match on television.
The National Police Chiefs’ Council (NPCC) said 387 football-related incidents were recorded at the weekend, mostly alcohol-related disorder.
Its Lead for Football Policing Deputy Chief Constable Mark Roberts, said: ‘There is absolutely no excuse for this type of senseless behaviour. Emergency services resources are already stretched.’