Officials confirmed there had been "an incident" at the outer security perimeter area, after footage showed a crowd of supporters making a mad dash to get inside.
But a spokesperson for Wembley Stadium said there had been no security breaches of people getting in without tickets.
They said: "We are dealing with an incident that occurred at the outer security perimeter area of the stadium, with support from police.
"Safety measures were quickly activated in the relevant areas and there were no security breaches of people without tickets getting inside the stadium."
The Metropolitan Police said they supported the security teams at Wembley Stadium.
Fans in Leicester Square were seen throwing bottles and cones and the area was left littered with rubbish.
Fans have been urged to stay safe and look after each other.
Police said there had been people "jumping off street lamps or hoardings" and warned "this could easily end in injury".
Huge crowds of people have been in party mode outside the stadium and across London throughout the day, proudly sporting the team colours and draped in England flags.
But some boisterous supporters even climbed on top of a bus outside Wembley, while others outside King's Cross station in the capital let off red and white smoke during the build-up.
British Transport Police said there had been "multiple cases of flares being set off within the vicinity of railway stations" in the capital and warned that "these incidents are offences and will be investigated".
Inside the stadium team captain Harry Kane and the rest of the squad looked relaxed as they took to the pitch ahead of the match shortly after their arrival at the famous ground.
They had been cheered as they set off from the team hotel for what the nation hopes will be a date with destiny against Italy.
Victory for England would mark the men's football team's first major tournament win since 1966 World Cup success, which also took place at Wembley.
Southgate has appealed to England's supporters to "respect the opposition", after booing could be heard during other teams' anthems at previous matches.
Reporting by PA