The behaviour of fans from both countries before and after their 1-1 draw at the Stade Velodrome in Marseille, was “unacceptable”, the executive committee of European football’s governing body said.
It opened disciplinary proceedings against the Russian Football Union yesterday for alleged crowd disturbances, racist behaviour and fireworks being set off by its fans during the game on Saturday night.
Uefa has no power to take action against England for the behaviour of fans in the streets of the city, where police used tear gas as hooligans battled over three consecutive days.
However, in a statement, it appealed to English and Russian officials to urge supporters to “behave in a responsible and respectful manner”.
It added: “Irrespective of any decisions taken by the independent disciplinary bodies relating to incidents inside the stadium, we will not hesitate to impose additional sanctions on the Football Association and Russian Football Union, including potential disqualification of their respective teams from the tournament, should such violence occur again.”
A Downing Street spokeswoman said last night that six British nationals remain in hospital following the violence in Marseille.
She said Home Secretary Theresa May had spoken to her counterpart in Paris, interior minister Bernard Cazeneuve, about the violence.
The spokeswoman said that, while UK officers have been in France since before the tournament, they had offered to send more “to support the security operation around the match in Lens”.
She added: “UK police will be assisting the French with their post-incident investigations and supporting them to gather evidence, including evidence against any England fans involved in the disorder.”
Russian sports minister Vitaly Mutko has also condemned the violence.
The incident raised serious questions about French security at a time when the country is on high alert after November’s terrorist attacks in Paris.
There were issues with segregation of fans, Uefa admitted, promising security would be “strengthened”.
The scenes in Marseille were described by the FA as “terrible” while world football body Fifa said it was “wholly unacceptable to see such shameful scenes around football matches perpetrated by a minority of idiotic troublemakers”.