The alleged incident took place in Auckland's Hilton Hotel
New Zealand police have yet to speak to four England rugby players under investigation after an alleged incident in an Auckland hotel last Sunday.
No formal police complaint has been lodged, and no details made public, but Auckland police are now in Christchurch to probe the "serious allegations".
The England team play the All Blacks in in the South Island city on Saturday.
Police have told the England management they want to speak to the players but "no arrangements" have yet been made.
The BBC's Nick Bryant, in Christchurch, said: "Detectives from the Criminal Investigation Bureau (CIB) - that is the country's serious crime squad - have travelled down from Auckland to Christchurch, and are ready and keen to interview the four England players.
"But that has not happened yet, and it is a source of mounting frustration within the investigation that there are no specific arrangements in place to facilitate that.
"The England players are not obliged to speak to the police, they cannot be compelled to do so. But clearly the New Zealand CIB wants that to happen sooner rather than later.
"There is mounting frustration within the CIB that the RFU are not making the players available at the moment.
"The RFU is sticking to the statement it released on Wednesday, saying it is co-operating with the police."
The alleged incident was said to have involved up to four players and occurred in a private room at the Hilton Hotel, in Auckland, early on Sunday after England's defeat in the first Test against New Zealand.
An Auckland police spokesperson said: "We have made it known to the England management via their representatives that we would like to speak with the team members.
"There are no arrangements to do so."