Sixteen fans were held at the stadium for climbing fences, possession of drugs or stealing tickets, the spokeswoman for the British team of police officers working in Germany said.
The 16 have now all been released with some fines.
Ten fans were picked up in the town, with six held for assault, one for drunkenness, two for working as ticket touts and one selling forged tickets.
The spokeswoman said these cases were still ongoing and it was not clear how many were still in police custody.
British police refer to the cases as arrests but in German law officers can hold people for several hours to allow them to calm down and these incidents are not always classified as arrests.
Some 50,000 England supporters were expected to be in the medieval city for the game. Those who did not get tickets watched the match on big screens and the evening passed off smoothly, with fans singing and drinking into the night.
Police patrolling the area looked relaxed, smiling and chatting to England supporters.
England play their last Group B match against Sweden in Cologne on Tuesday.