A Welsh MP who believes he was a victim of phone hacking by the News of the World has reiterated his call for a judicial review.
The newspaper is to apologise for the scandal and is to set up a compensation fund.
Rhondda Labour MP Chris Bryant said it was "just the start of the story."
He said he had "anxieties" about previous investigations into phone hacking undertaken by the Metropolitan Police and wants a judicial review.
News International, which owns the newspaper, is offering to pay damages to eight well-known people who brought civil actions claiming their mobile phones were hacked.
The BBC's business editor Robert Peston said News International was offering to settle with names such as former Culture Secretary Tessa Jowell, designer Kelly Hoppen and sports commentator Andy Gray.
In addition to Sienna Miller, the others are believed to be David Mills, lawyer and Mrs Jowell's estranged husband; Joan Hammell, former aide to former Deputy PM John Prescott; Nicola Phillips, assistant to publicist Max Clifford; and former Olympian and talent agent Sky Andrew.
It is understood the company is setting aside £20m in a compensation fund.
News International says its previous inquiries into the allegations were "not robust enough" and failed to uncover important evidence.
It had previously insisted phone hacking was the work of one reporter.
Speaking to BBC Radio Wales, Mr Bryant said: "They argued for a long time that there were very few victims - that there was just one rogue reporter - that they had done a full investigation and all that proves to be untrue.
"One of my anxieties is the police didn't do a full investigation in 2006, 2009 and 2010 when lots of people were calling for a full investigation.
"Consequently we still don't know the full level of the criminality that went on at the News of the World and in fact many of the victims themselves don't know they were involved.
"I think this is just the beginning of the story.
"I'm seeking a judicial review of the Metropolitan Police's activity.
"I have a big anxiety about why the Metropolitan Police didn't do a proper investigation themselves."
Last week Acting Met Deputy Commissioner John Yates told the Culture, Media and Sport Select Committee that there was no cover up of the phone hacking scandal.
He said only "a very small number of cases" of phone hacking could be proven.
Asked by Labour committee member Tom Watson whether he had suppressed wrongdoing by News of the World journalists, Mr Yates said: "Absolutely not."