News of the World hacked murdered girl's phone-lawyer
* Girl's disappearance prompted nationwide search
* Police investigating illegal phone hacking by the paper
* UK close to approving News Corp buyout of BSkyB
LONDON, July 4 (Reuters) - A private detective working for Britain's News of the World tabloid hacked into voicemail messages left on the mobile phone of a murdered schoolgirl while police were searching for her, a lawyer for her family said on Monday.
Mark Lewis, of solicitors Taylor Hampton, said police investigating phone hacking by the paper had told the parents of Milly Dowler that their daughter's own phone had been intercepted illegally.
He said the family planned to sue the paper, owned by News International, part of Rupert Murdoch's News Corp .
The disclosure comes days after British government gave its backing for News Corp to buy out British pay-TV group BSkyB, rejected complaints the move would give Murdoch too much power and influence.
The government has announced a final consultation period until July 8 to consider further undertakings to guarantee the editorial independence of BSkyB's Sky News.
Five people have been arrested by detectives investigating assertions that journalists on the News of the World hacked the phones of members of the royal family, politicians, celebrities and sports stars to listen to their voicemail messages.
The paper said in April it would admit liability and pay compensation in eight cases, although lawyers say many more suspected victims will seek compensation.
Milly Dowler, a 13-year-old schoolgirl from Surrey, south England, disappeared in March 2002, prompting nationwide search. Her bones were found six months later in a wood. Last month a former nightclub doorman was convicted of her murder.
"Who was at the News of the World thinking it was appropriate to try and hack into the phone of a missing young girl?" Lewis told BBC television.
"It is distress heaped upon tragedy to learn that the News of the World had no humanity at such a terrible time.
"The fact that they were prepared to act in such a heinous way that could have jeopardised the police investigation and give them false hope is despicable," he added.
Opposition Labour politician and former deputy prime minister John Prescott said it was not too late for the government to hold up the News Corp-BSkyB deal.
"These people are not fit and proper persons to be running our major media," he told BBC radio.
The government has said the hacking investigation will not affect its decision on BSkyB, saying that was related solely to the issue of media plurality.
A spokesperson for News International said it had been cooperating with the police investigation.
"This particular case is clearly a development of great concern and we will be conducting our own inquiries as a result. We will obviously co-operate fully with any police request on this should we be asked," the spokesperson said.