The Metropolitan Police arrested 25 people in central London and a further five in the vicinity of Wembley Stadium, where the two British sides met for the first time in a major international tournament for a quarter of a century on Friday.
Scotland Yard said in a tweet: “Thirteen arrests were for public order offences, six for drunk and disorderly, four for assault on police, three for assault, two related to class A drugs and one each for breaching a dispersal order and breaching a banning order.”
Red flares were set off as crowds gathered in Leicester Square for the much-anticipated match.
Many fans wore kilts and draped themselves in Scotland flags, as they sang and cheered in the popular tourist spot.
Others kicked footballs, some held aloft bottles of alcohol and many belted out the Scottish national anthem and chanted, “No Scotland, no party”.
In anticipation of clashes, the Met issued a section 35 dispersal order to remain in place until 3pm on Saturday.
The force said officers entered Leicester Square at about 12.45am and encouraged those still at the scene to leave the area.
Uniformed officers formed a line to separate Scotland and England fans.
The square finally cleared by 1.15am.
Additional reporting by Press Association