World Rugby is investigating England's coaching staff for an alleged breach of rules during Saturday's defeat to Australia.

A report in Australia states two members of the coaching team approached match officials in the tunnel at Twickenham at half-time. The loss to the Wallabies meant the hosts were dumped out of the tournament with one pool match still to play.

"World Rugby is investigating an alleged breach by the England coaching team of the match-day communications protocol between match officials and team members or union officials during the match between England and Australia," a World Rugby Statement read.

Stuart Lancaster's coaching staff will be under investigation Andrew Matthews / PA Wire/Press Association Images

England trailed 17-3 at half-time of the match and as the teams ran off the pitch, the coaches are reported to have spoken to officials in contravention of regulations.

"The protocol prohibits certain conduct on match days including coaches approaching match officials during a match or at half-time during a match," World Rugby's statement continued.

Wallabies coach Michael Cheika received a formal warning from Super Rugby governing body SANZAR earlier this year after an investigation into him approaching referee Jaco Peyper at half-time during his NSW Waratahs' win over the Blues in Sydney.

The SANZAR investigation found Cheika had a "short and polite exchange" with Peyper to clarify a scrum interpretation, but that there was no evidence the referee was influenced by the exchange in his handling of the match.