LONDON--The U.K. government is reviewing its procedures for crank calls--and has warned its departments to be alert--after a hoax caller claiming to be the head of Britain's GCHQ intelligence agency was put through to Prime Minister David Cameron on Sunday.

And earlier on Sunday, a call to GCHQ resulted in the disclosure of a mobile phone number for the organization's director, Robert Hannigan, Mr. Cameron's office said in a statement.

"In neither instance was sensitive information disclosed," said the prime minister's office, which is also known as Number 10.

The two calls represent an embarrassing public lapse at a time when British authorities are at a heightened level of security due to the perceived threat of a terror attack.

"Both GCHQ and Number 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," Number 10 said.

Nobody has claimed responsibility for the calls and it is not clear whether the two calls are connected.

A government spokeswoman declined to give any details of the calls or the exchange with the prime minister.

"The prime minister ended the call when it became clear it was a hoax," Number 10 said.

The statement said the mobile phone number that GCHQ had provided the hoax caller for the agency's director, "is never used for calls involving classified information."

Nobody was immediately available at GCHQ to comment.

Number 10 has been the target of hoax calls in the past, but not for some time. In 1998 a radio DJ pretending to be an opposition leader was put through to Prime Minister Tony Blair, the BBC reported.

Write to Nicholas Winning at nick.winning@wsj.com

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