The prime minister ended the call when it became clear that it was a hoax and no sensitive information was disclosed, the Downing Street said.
However, the giggling prankster - who claimed to be Robert Hannigan, director of British intelligence agency GCHQ (Government Communications Headquarters) - telephoned The Sun tabloid and said he will "definitely do it again" as it was "so easy" to make the hoax call.
The man allegedly rang up the newspaper to boast "I've just made monkeys out of GCHQ", minutes after his phone conversation with Cameron.
"In the first instance, a call was made to GCHQ which resulted in the disclosure of a mobile phone number for the Director. The mobile number provided is never used for calls involving classified information," a government spokeswoman said in a statement.
"In the second instance, a hoax caller claiming to be the GCHQ director was connected to the Prime Minister. The Prime Minister ended the call when it became clear it was a hoax.
"In neither instance was sensitive information disclosed," the spokeswoman said.
Following the two incidents, a notice went out to all departments to be on alert for the possibility of more fake calls.
He told the newspaper the situation was "hilarious" and added: "I'm definitely going to do it again. It was so easy."
He is understood to have said Hannigan was needed at a security meeting but was not answering his "usual number".
Authorities are now reviewing procedures, both at the PM House, 10 Downing Street and GCHQ, to help ensure that such calls are not patched through again, the spokeswoman said.
"Both GCHQ and No 10 take security seriously and both are currently reviewing procedures following these hoax calls to ensure that the government learns any lessons from this incident," he said.
The call to the prime minister was made to an official mobile but the conversation was understood to have been "quite brief" before the hoax was discovered.
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