Updated with further information on the News of the World hacking scandal, and the arrest of Andy Coulson, the former editor of the newspaper

LONDON ( TheStreet) -- British Prime Minister David Cameron called for a "full public inquiry" led by a judge into the hacking scandal that forced News Corp. ( NWSA - Get Report)to shut down News of the World .

The newspaper's last issue will be Sunday.

The public inquiry will take place once police in London finish their investigation into whether the newspaper made illegal payments to officers for confidential information.

Cameron's comments Friday were made prior to the arrest of his former communications chief and former News of the World editor Andy Coulson over the alleged phone hacking and illegal payments. Coulson, editor of the newspaper from 2003 to 2007, was in custody at a London police station.

In a Downing Street press conference, Cameron said hiring Coulson was his decision, adding "I take full responsibility for it."

Cameron also said Friday Rebekah Brooks, a former editor of News of the World, should have resigned as CEO of News International, the British unit of News Corp., amid the hacking scandal. If Brooks offered her resignation to him he would have accepted, Cameron said.

Rupert Murdoch, the owner of News Corp., has stood by Brooks.

Cameron also said the U.K. government would follow the proper procedures in making a decision of News Corp.'s acquisition of British Sky Broadcasting ( BSY).

"Governments must follow the proper legal processes and procedures. That is exactly what Jeremy Hunt is doing, Cameron said of the U.K.'s culture secretary. "His role is to take the advice of independent regulators. And, as his department made clear this morning, given the events of recent days, this will take some time."

Hunt echoed the prime minister's statements, saying the volume of responses to a public consultation, said to exceed 100,000 submissions, would delay the BSKYB sale process, The Associated Press reported.

-- Written by Joseph Woelfel

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