Police have arrested 86 people so far following Sunday’s operation after the fall out of the Euro clash.
As many as 53 of these arrests were made at Wembley, police said.
In total across the tournament there have been more than 130 arrests.
There were 19 officers injured during violent scenes outside Wembley stadium and in central London.
People were arrested on charges including: public order offences, ABH, drunk and disorderly and criminal damage.
Deputy Assistant Commissioner Laurence Taylor said: “Throughout the course of the Euros tournament, the vast majority of people have watched the matches responsibly and safely, and enjoyed the build up to last night’s final.
“However, the unacceptable scenes we saw yesterday were a small number of people intent on using the football as an excuse to behave appallingly towards other members of the public and officers.
“The reports of online hate crime abuse are utterly abhorrent and totally unacceptable. We have launched a post-event investigation and will actively pursue and investigate offenders and criminal offences.“This behaviour is not welcome in London and I urge anyone who is being subjected to any abuse, both online and in person, to contact police and report it so the police can investigate thoroughly and accordingly.”
Questions were asked about policing of the game and stadium security after video showed ticketless fans fighting with stewards and pushing through barriers at Wembley before the match.
Riot police broke through crowds outside the stadium when fans left the game, with some throwing bottles and chanting anti-Italian slogans after England lost on penalties.
Watch: Watch England fans clash with police outside Wembley
The mood was equally edgy at Trafalgar Square when supporters filed out following the defeat with some swearing, smashing bottles and overturning bins.
Others kicked and smashed the fences around the fan zone.
A spokesperson for Wembley Stadium said they had dealt with “an incident that occurred at the outer security perimeter area of the stadium, with support from police”.
Former player turned pundit Chris Kamara said he had an “horrendous walk down Wembley way” and had to dodge bottles being thrown by the crowd.
Some inside Wembley said fans had been standing on the concourse for the entire first half, watching the match.â Supporters who left their seat at half time were asked to show a ticket before returning, one said.
Earlier in the day fans threw bottles in Leicester Square as trouble broke out hours before the final.
The Met also said some England supporters without tickets were attempting to enter the Trafalgar Square fan zone.
The force tweeted: “A large crowd of fans have gathered near to the fan zone in Trafalgar Square attempting to push in without tickets.
“There are no more tickets or seats available in the fan zone. We’re engaging with this crowd and telling them to disperse.”
It comes after fans gathered in Leicester Square threw bottles and plants across the street and pushed over bins.
Smoke from the flares are believed to have triggered fire alarms, with passengers initially advised to change their journeys.
British Transport Police said they received reports of an incident at 12.40pm and the station was reopened at 1.07pm.
Watch: Gary Neville criticises Boris Johnson after racist abuse of England players