He writes: "Executives at News are engaged - they tell me - in finding out everything they can about who was hacked by the News of the World, News International's Sunday tabloid, and who at News International knew about the hacking.
"Once they have the details, they will offer settlements to those celebs, politicians and others whose privacy may have been invaded - to cut out the requirement for huge lawyers' fees. Any culpable News International executives will be sacked."
But Peston predicts in won't end there: "Not too subtly, the message will be sent out that if News International's Augean Stables have been cleaned, what about the stench from other media groups? Because, as I've mentioned before on this blog, there was a period at the start of this century when questionable techniques to obtain stories were employed by a number of newspapers.
"In this context, it matters that Mark Lewis - the solicitor who obtained a whopping settlement from the News of the World over the hacking of the phone of Gordon Taylor, the chief executive of the Professional Footballers' Association - is preparing cases for clients alleging unlawful breach of privacy against media groups other than News International."
Peston adds: "Not to over-dramatise, this has all the potential for the newspaper industry to turn into its version of the MPs' expenses scandal."