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Wembley Stadium said no ticketless fans managed to gain entry after video footage showed dozens of people pushing through barriers.
Fans fought with stewards and police as they attempted to break through the gates before the Euro 2020 final.
A spokesperson for the stadium said "safety measures were quickly activated" after the incident.
"There were no security breaches of people without tickets getting inside the stadium", the spokesperson said.
The Met Police said: "We supported the security teams at Wembley Stadium a short time ago with this incident.
"Wembley security officials have confirmed there was no security breaches of people without tickets getting inside the stadium."
A large crowd was also trying to enter the fan zone in Trafalgar Square without tickets shortly before kick-off, the Met Police said.
Police said they were "engaging with the crowd and telling them to disperse".
At Wembley, a man was taken to hospital after he was hit by a bus on High Road. Police said the bus driver stopped at the scene and the man's injuries are not said to be life-threatening.
In footage taken at Wembley Stadium and posted by video blogger Paul Brown, fans could be seen jumping over barriers and grappling with stewards and police, as some of them were ejected.
Mr Brown said there were not enough police to deal with the size of the crowd.
Police can’t stop the England 🏴 fans without tickets storming the ticket entrances at Wembley – not enough riot police to deal with the weight amount of the crowd – kicking off !!! pic.twitter.com/ZM7KpbMmQJ
— Paul Brown 🇬🇧 Browns fan🏈 London News 🎥Vlogger (@PaulBrown_UK) July 11, 2021
The BBC is not responsible for the content of external sites.View original tweet on Twitter
BBC News producer Warren Moran said he saw people without tickets forcing their way through the turnstiles, but could not say whether they were later ejected from the stadium.
He said dozens of people were pushing through the gates for disabled people, which were open.
A video posted by Sky Sports reporter Michelle Owen showed several fans streaming over barriers as stewards looked on.
She said: "If this is even crossing your mind, don't. You don't get far. Please don't ruin it for everyone at Wembley."
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Wembley said the incident took place at the outer perimeter and police had supported stewards in responding to it, without fans breaching security.
Despite Wembley's assertion that ticketless fans had not gained entry to the stadium, some witnesses said they had seen people getting in by "tailgating" behind ticket-holders through the barriers.
The Daily Telegraph's Ben Rumsby posted on Twitter that he and others had seen examples of this in the build-up to the final.