"The royal family have been clients of the (hospital) for many, many years and it beggars belief that a member of the public could call up and obtain details of the duchess' medical condition in this way.
"Where on earth were the checks and balances? The hospital will be livid at what has happened and I am sure the palace will be demanding answers."
A spokesman for the hospital labelled the act "foolish" and said advice was being sought about whether legal action should be taken against the broadcaster.
A legal expert told British tabloid The Sun: "It would be open to the attorney-general to consider the possibility of a prosecution for treason."
"To impersonate the monarch is to suggest that you are the monarch and the true monarch doesn't exist," the lawyer said, adding that the offence of treason extends to citizens of commonwealth countries, including Australia.
Greig and Christian have apologised for the prank and sent their best wishes to Catherine.
The call was not the first successful royal hoax.
In 1995, a Canadian DJ spent 14 minutes chatting with the Queen, at times in fluent French, after being connected by the Buckingham Palace switchboard.
Catherine showed no signs of being upset by the prank as she left hospital on Thursday morning (GMT).
Wrapped in an overcoat and scarf and carrying a bunch of yellow flowers, Catherine smiled as she stopped briefly on the hospital steps before entering a waiting Jaguar accompanied by William.
A statement from royal aides said the Duchess would spend coming days resting at her London home, Kensington Palace.
- AAP