UK police seek evidence in newspaper phone snoop case

* Detectives ask Murdoch paper for new details

* Police under pressure to act after editor's suspension

LONDON, Jan 7 (Reuters) - British police asked a newspaper on Friday for new evidence about accusations of illegal phone eavesdropping by its staff, in a case that has caught up Prime Minister David Cameron's communications chief.

Government communications chief Andy Coulson quit as boss of the News of the World in 2007 after one of the paper's reporters was jailed for secretly listening to phone messages of royal household staff to get scoops on Queen Elizabeth's family.

The paper, part of Rupert Murdoch's News Corp media empire, had always said the jailed reporter was a rogue employee acting alone, but this week it suspended a senior editor.

British media say the editor, Ian Edmondson, was named in documents uncovered in a lawsuit by film star Sienna Miller, who accuses the paper of hacking into her voicemail account to hear her messages. Edmondson reported to Coulson at the time.

"The MPS has this evening written to the News of the World requesting any new material they may have in relation to alleged phone hacking following the suspension of a member of their staff," the Metropolitan Police Service said in a statement.

Coulson says he knew nothing of wrongdoing at the paper when he ran it.

Police said last month there was not enough evidence to charge Coulson with a crime [ID:nLDE6B91FB], but critics say the force may have overlooked some evidence. The opposition Labour Party called on Thursday for a new police probe, to look into evidence emerging in private lawsuits like Miller's.

The on-and-off girlfriend of fellow star Jude Law, Miller complains that her private life became fodder for tabloids like the News of the World, Britain's largest-selling Sunday paper, which used dirty tricks to find out about her affairs.

British authorities are currently deciding whether News Corp (NWSA.O) should be allowed to buy out the remainder of pay TV company BSkyB in a $12 billion deal. Murdoch's critics say it would concentrate too much power in his group's hands.

(Reporting by Michael Holden; Editing by Peter Graff)