The Second Part of the Leveson enquiry was “ to examine the extent of unlawful or improper conduct at the News of the World and other newspapers, and the way in which management failures may have allowed it to happen”.
A direct quote from the inquiry (bonding is mine):
This Inquiry was ultimately directed because of the wide scale public revulsion at the reported conduct of one or more journalists from the News of the World (NoTW) in intercepting messages left on the mobile telephone of Milly Dowler: this type of interception has been referred to colloquially as phone hacking. Having said that, however, there was also increasing public concern about the apparent lack of appropriate investigation by the Metropolitan Police Service (MPS) into the conduct of a private investigator, Glenn Mulcaire,
and the extent of the involvement of the NoTW (precipitated by increasing disclosure arising out of civil litigation). The consequence (prior to the disclosures about Milly Dowler) was that the then Acting Commissioner, Tim Godwin, had re-opened the investigation into the NoTW which had started in 2006; substantial resources were devoted to it….
That 2006 investigation into the operations of Glenn Mulcaire was known by the police as Operation Caryatid. It was launched by the Police after Prince William and his office raised concerns directly with Scotland Yard about William’s phone being hacked back in December 2005.
As you can see, this investigation was credited by Lord Leveson as being a one of the keys events, along with the hacking of Dowling’s phone, that led to his inquiry.