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Mel Greig and Michael Christian from 2Day FM posed as the Queen and Prince Charles during the phone call to King Edward VII Hospital on Tuesday evening (AEDT) and were put through to a nurse who gave an update on the Duchess's condition.
"We were very surprised that our call was put through. We thought we'd be hung up on as soon as they heard our terrible accents," the broadcasters said in a statement.
"We're very sorry if we've caused any issues and we're glad to hear that Kate is doing well."
The prank call was pre-recorded and vetted by lawyers before being broadcast to listeners in Sydney.
"2Day FM sincerely apologises for any inconvenience caused by the inquiries to Kate's hospital," a station spokeswoman said.
"The radio segment was done with lighthearted intentions. We wish Kate and her family all the best and we're glad to hear she's doing well."
The pair adopt toffy accents for the call, during which the nurse refers to Greig as "ma'am", while a third member of 2Day FM staff can be heard pretending to bark in an attempt to impersonate one of the Queen's corgis.
"She's quite stable. She hasn't had any retching and she's been sleeping on and off," the nurse tells the pranksters after referring to Greig as ma'am.
A hospital statement released on Wednesday said the incident has sparked a review of telephone protocol.
"King Edward VII's Hospital Sister Agnes can confirm that an Australian radio station made a hoax call to the hospital in the early hours of Tuesday morning," the statement read.
"This call was transferred through to a ward and a short conversation was held with one of the nursing staff. King Edward VII's Hospital deeply regrets this incident."
John Lofthouse, chief executive at King Edward VII's Hospital, said: "This was a foolish prank call that we all deplore. We take patient confidentiality extremely seriously and we are now reviewing our telephone protocols."
Catherine was admitted to the facility, favoured by the royal family, on Monday as the world learnt she was in the early stages of pregnancy.
She is being treated for acute morning sickness and is expected to be in hospital for several days, the palace said.
Representatives for the Duke and Duchess of Cambridge have not commented on the prank.
The segment of Tuesday evening's radio show can be heard online by visiting www.youtube.com/watch?v=wa5JQC8VNdw
Greig asks the nurse when she can visit her "granddaughter Kate" and how her "little tummy bug is going".
"When is a good time to come and visit her coz I'm the Queen and I need a lift down there ..."
She is then heard to ask Charles (Christian) when he can take her to the hospital.