The Guardian, The Daily Telegraph and The Independent newspapers all devoted their front pages today to allegations that investigator Glenn Mulcaire intercepted frantic messages left by relatives for the 13-year-old when she went missing in 2002, while working on behalf of the News of the World.
Baker, who recently got the all-clear in his battle with cancer, however feels that the story has not been given sufficient priority by most of the press.
> News International boss Rebekah Brooks "sickened" by Milly Dowler hacking claims
> Hugh Grant: 'News of the World investigator told to hack Milly Dowler phone'
Writing on Twitter, he posted: "The #notw story is a genuine and disgusting scandal. Yet most papers aren't giving it anywhere near front page [on Tuesday]. Rot in hell hacks."
Lawyers representing the family claim that the alleged hacking dated back to the time when Rebekah Brooks was editor of the News of the World. Brooks is now News International's chief executive.
BBC business editor Robert Peston said that Brooks is expected to tell staff that she is "deeply shocked" by the claims, but will insist that she knew nothing about phone hacking at the newspaper.
Prime Minister David Cameron said that the allegations against the News of the World were "quite shocking" and would be a "truly dreadful act" if proved true.
Labour leader Ed Miliband described the alleged hacking as a "cruel and immoral act" and said that the ongoing police inquiry into the newspaper must "get to the bottom of who was responsible for this and who was complicit in it".