Wayne Couzens was jailed for life last month after using his position as a serving officer to abduct marketing executive Sarah Everard on a London street in March before raping and murdering her in a case that shocked the United Kingdom and stirred protests over violence against women.

One of the Independent Office for Police Conduct's (IOPC) investigations involved allegations that a probationary officer had used WhatsApp to share what was described as a highly offensive and inappropriate graphic, depicting violence against women, with colleagues.

"Our investigation... indicated that the graphic was intended to be in reference to the kidnap and murder of Sarah Everard by a serving officer. We established that the officer was off duty at the time but went on to staff a cordon as part of the search for Ms Everard," the IOPC said.

In a separate investigation, the IOPC looked at allegations that officers from several forces breached standards of professional behaviour when they used the Signal messaging platform to share information connected to Couzens' prosecution.

The Everard case has fuelled a debate on how police forces vet recruits and whether a misogynistic culture exists.

"The allegations involved in these two investigations, if proven, have the capacity to further undermine public confidence in policing," IOPC Regional Director Sal Naseem said in a statement.

"They also once more illustrate the potential consequences for officers and come at a time when policing standards and culture have never been more firmly in the spotlight."

The watchdog said it was still looking at how two police forces handled allegations of indecent exposure now linked to Couzens in 2015 and earlier this year.

Australian Associated Press