A minority of celebrations caused significant disorder, leading to criminal damage, blocked roads and anti-social behaviour, the National Police Chiefs' Council (NPCC) said in a statement.
Its 44 forces across England and Wales recorded 387 incidents and made more than 70 arrests over the weekend for mostly alcohol-related disorder.
"Numerous roads across the country were blocked, stopping emergency vehicles getting to people in need and an ambulance is now off the road while being repaired," said Deputy Chief Constable Mark Roberts, the NPCC Lead for Football Policing.
He said shops were damaged and people abused and assaulted, while other fans climbed on buses and cars, causing damage to the vehicles and in some cases themselves.
“This is in stark contrast to the (England) fans out in Russia, whose behaviour, apart from a couple of minor incidents, has been great."
The NPCC has recorded 1,086 football-related incidents since the tournament began on June 14, including 226 of domestic abuse, and 230 arrests.
In advance of England's semi-final against Croatia on Wednesday, the national team's biggest match for 28 years, Roberts appealed for revellers to behave.
"We want people to celebrate ...but not at the expense of law-abiding fans and emergency services’ resources," he said.
(Reporting by James Davey, editing by Andy Bruce and John Stonestreet)
