I think the broadsheets are probably clean, or at least, they broke laws for good reasons compared to the tabloids. Bear in mind that newspapers break the law in pursuit of stories all the time. The Guardian
with PRISM, the Times
with Scargill's Gadaffi connection, and the Telegraph
with MPs' expenses. The point is that sometimes breaking the law in pursuit of a story that's actually in the public interest is okay. The tabloids broke the law for sheer trivialities.
The thread the unravelled this whole thing was Clive Goodman getting caught hacking Clarence House's phones: he actually quoted voicemail messages. All this for a page 5 lead about Wills spraining his ankle! It's pretty clear that it became standard investigative practice at the red tops, and nobody stopped to say "guys, this is really fucking illegal and it could backfire horribly on us at any time." I'm sure the quality press know exactly
how to hack phones, and I bet they have done at some point. But they probably have the sense not to do it as a fishing technique for pathetic stories as the tabloids did.