Hundreds of fans without tickets broke through security barriers to get into Wembley Stadium in a bid to watch Sunday's European Championship final against Italy.
UEFA on Tuesday asked an investigator to study violence by England supporters at the game.
The English Football Association has been separately charged with multiple offences by fans before and during their team's loss to Italy in a penalty shootout after a 1-1 draw.
UEFA's charges against England's FA also relate to booing Italy's national anthem, a fan who stopped play by running on the pitch, throwing objects, and lighting fireworks.
The official attendance was around 67,000 of the stadium's 90,000 capacity, with many seats intended to be left empty to distance fans during the COVID-19 pandemic.
But there was extremely high demand for tickets for England's first major tournament final in 55 years.