The call by Mel Grieg and Michael Christian to King Edward VII hospital where Kate Middleton was being treated for acute morning sickness had resulted in the suicide of nurse Jacintha Saldanha, who fell for the prank and put the call through to the Duchess of Cambridge's ward.
The Metropolitan police have now passed the case file to their colleagues in Australia to see if the pair broke any laws there.
The news comes as it emerged that Mel Grieg has decided to take legal action against her employer, 2Day FM, for "failing to provide a safe workplace".
The hoax, which was broadcast on the radio programme in Australia, sparked worldwide outrage after Saldanha was found hanging in the hospital's nurses' quarters days later.
An inquest into her death is scheduled to begin in September and Grieg has offered to give evidence.
"The decision by Ms Greig to sue the radio station is brave, although it comes as no surprise. Ultimately the radio station made the decision to broadcast the hoax call and must bear responsibility for the tragic death of Jacintha," said British Indian MP Keith Vaz, who has been supporting the Saldanha family through the tragedy.
Scotland Yard had investigated whether the DJs could be charged with any offence under the Malicious Communications Act. But in February the Crown Prosecution Service (CPS) announced that prosecution would not be in the public interest.
"However misguided, the telephone call was intended as a harmless prank. The consequences in this case were very sad," a CPS spokesperson had said at the time.
Greig's lawyer, Steven Lewis from Slater & Gordon, said in a statement: "I can confirm that a general protections application has been filed with Fair Work Australia on behalf of Mel Greig against Southern Cross Austereo alleging the radio station failed to maintain a safe workplace".
Christian has since resumed work and was last month awarded a national "top jock" prize by the broadcaster.
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