Football Association chief executive Martin Glenn has written to England supporters warning them further disorder at Euro 2016 will not be tolerated.
Glenn has urged fans in France ahead of Thursday's game against Wales "to act in a positive and respectful way".
England have been warned they could face expulsion from the tournament if the violence which has surrounded their early involvement continues.
Ugly scenes involving supporters in Marseille dominated the build-up to last Saturday's game against Russia.
English supporters have also been the victims of violent attacks from Russian supporters, including inside the stadium. That has led to Russia being given a suspended disqualification from the tournament by organisers UEFA.
There have been repeated calls for calm, and for increased security, ahead of the Wales game in Lens.
In a letter to members of the England Supporters Travel Club, Glenn wrote: "We recognise that some of you were subjected to acts of violence from rival supporters in the stadium last weekend. It was truly appalling behaviour but you reacted admirably in difficult circumstances. We acknowledge UEFA's ruling against the Russian Football Union today.
"Turning towards ourselves, you will be aware that UEFA has warned us of our fans' contribution to the anti-social and violent scenes in Marseille leading up to the Russia match. It is something we take very seriously and while tens of thousands of you acted impeccably, there was a minority that did not.
"Like the England team, you represent the badge and I urge you to act in a positive and respectful way."
He added: "Anti-social behaviour will not be tolerated and we will work with the relevant authorities to identify those supporters involved and issue sanctions where appropriate to our members.
"UK police also will monitor any such behaviour and those committing offences could face arrest or additional sanctions such as football banning orders when they return home.
"I ask you all to take heed of the advice being given and to continue to respect our hosts in France."
With Russia playing on Wednesday in nearby Lille, where many England fans are staying, a high-level security meeting has been held between UEFA, French authorities, UK police and the FAs of England and Wales.
Glenn says this will result in a "larger, more visible police presence in both Lens and Lille".
Glenn also points out that a series of restrictions regarding the sale and consumption of alcohol will also be imposed.