The assailant of the attack, which took place in Sao Paulo during England's 2-1 defeat against Uruguay, has yet to be identified.
Football pundit Stan Collymore had initially tweeted to say that he had seen footage of the incident, while the Association of Chief Police Officers later verified the claim.
Chief superintendent Rachel Barber is quoted by BBC Sport as saying: "In the immediate aftermath, we managed to make contact with the victim and offered advice and support. The day after the attack, the victim chose to make a formal complaint to the local police, and they opened an investigation.
"During the course of our pursuit of the assailant, we located and interviewed several witnesses. They were very helpful in giving their version of events, but, unfortunately they were unable to give us a name for the alleged attacker.
"Efforts are ongoing to identify the suspect and bring him to justice either in the UK or, if possible, back in Brazil where the offence occurred."
Six British police officers have travelled over to Brazil for the World Cup.