The Metropolitan Police had earlier told the inquiry that, while they had evidence that Dowler's phone was hacked, it was not conclusive whether or not any messages had been manually deleted.
David Sherborne, the lawyer representing the Dowler family, criticised the failures of the Surrey police in investigating the News of the World in 2002, the Metropolitan police decision to close its first investigation into hacking in 2006, and also the concealment of hacking by the News of the World itself.
Sherborne also claimed that the Leveson Inquiry into press ethics would have taken place irrespective of The Guardian's July 2011 article which included the later disputed claim of manual deletions of Dowler's messages.
"The News of the World did hack into Milly Dowler's phone searching for a scoop at a time when she had already been murdered. That fact alone is horrifying enough," he was quoted by The Guardian as telling the inquiry.
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"We also know that the newspaper interfered seriously with the police investigation, trying to use the information they had illegally obtained to get an exclusive on Milly's movements.
"The 'false hope' moment and the News of the World's potential responsibility was not part of the decision to set up this inquiry in the first place."
He then read a statement from the family which again criticised Surrey Police for not taking the issue further in 2002, a course of action which might have prevented others from having their phones hacked.
"Police neglect and deference meant that it took the relentless efforts of one journalist to uncover what the police knew had gone on," Sherborne read.
"Whilst we would never have wished to have been thrust into the middle of this extraordinary scandal on top of what we have already had to deal with as a family, we continue to have faith that his efforts and the efforts of the inquiry and Operation Weeting will have a lasting positive impact."
The Guardian also issued a response to the issue of the hacking of Milly Dowler's phone and the matter of whether or not messages were manually deleted.