The videos are understood to have been taken at a Duke St property in the early hours of this morning.
Dunedin police said they had not received any complaints about the incident.
The England team's manager Jon Roberts said they were aware of the incident.
"It is being dealt with internally with the person involved and they will be disciplined."
The players had been given permission to go out after last night's game, he said.
"On behalf of England Rugby League, we apologise for the behaviour and have arranged for the repair of the small amount of damage," Mr Roberts said.
"We have had a great time in Dunedin and the city has made us welcome. Last night's match was a great spectacle for International Rugby League and we look forward to returning to the city in the future."
The team went to the Wingatui races in Dunedin on Tuesday, but had to leave because of the antics from a group of drunk students.
Hooker Daryl Clark told The Daily Star he had never seen as many drunk people in my life.
"We were all sober so it was a bit of an eye-opener. We didn't stay too long when we realised what it was like."
Watch: England league star's smashing entrance Part 2
In 2011, a touring England rugby union team got into trouble as a result of drinking antics.
A night out in Queenstown saw Mike Tindall captured in an embrace with someone who wasn't his wife put the UK tabloids into a frenzy. His wife, of course, is Princess Zara, granddaughter of the Queen.