LONDON (Reuters) - All those responsible for wrongdoing at the News of the World newspaper should be brought to justice, a spokesman for British Prime Minister David Cameron said after Rupert Murdoch's News Corporation announced it would close the tabloid.

"What matters is that all wrongdoing is exposed and those responsible for these appalling acts are brought to justice," the spokesman said.

"As the Prime Minister has made clear, he is committed to establishing rigorous public inquiries to make sure this never happens in our country again."

The decision to close the paper came as allegations mounted that its journalists had hacked the voicemails of thousands of people, from child murder victims to the families of Britain's war dead.

Cameron on Wednesday announced that there would be public inquiries into the paper and media ethics.

However, leader of Britain's opposition Labor Party Ed Miliband said the furor over the scandal would not die down until News International sacked top executive and Murdoch confidante Rebekah Brooks.

She edited the paper a decade ago during the period of some of the gravest allegations.

"The one person who seems to be staying her job is the chief executive of News International who was editor at the time that Milly Dowler's phone was hacked," Miliband told Sky News.

"I don't think News International can hope to start moving on and deal with these issues while she remains in post."

(Reporting by Michael Holden, editing by Keith Weir)