RFU elite rugby director Rob Andrew said England were fully co-operating with police in the matter and that the four players had the "complete support" of the team and management.

He said: "The England rugby team has been informed by Auckland Police that an allegation has been made against four members of the England playing squad. Whilst no formal complaint has been made, we are co-operating with the police and their inquiries."

He added: "The players concerned have the complete support of all the players and the management. In the circumstances, we are unable to make any further comment."

According to reports, the incident involved a woman, but Auckland Police said a formal complaint had yet to be lodged.

The alleged incident occurred in a private room while the team were staying at the Hilton Hotel in Auckland during the early hours of Sunday morning, local time, after England's 37-20 defeat to the All Blacks.

The England team are currently training in Christchurch on New Zealand's South Island ahead of the Second Test against the All Blacks on Saturday.

A spokeswoman for Auckland Police would not confirm the nature of the allegation or the identity of the players, but she said that no formal complaint had yet been made.

A police statement read: "Auckland City Criminal Investigation Branch is investigating an allegation involving up to four members of the England rugby team. The incident being investigated is alleged to have occurred early on Sunday, June 15, in a private room.

"Whilst an allegation was brought to the attention of police on Sunday evening, no formal complaint has been received. Investigating officers are receiving the appropriate level of co-operation from the England rugby team management."