The owner of The News of the World is hoping its admission that at least eight people - which the BBC understands includes the actress Sienna Miller and the former culture secretary Tessa Jowell - had their mobile phone voicemails hacked into will start to draw a line under the scandal.
News International has apologised and set up a fund to deal with what are described as "reasonable claims" for compensation.
Speaking on the programme, Guardian editor Alan Rusbridger, who has been pursuing the story for several years, said it was likely that many more claims for compensation could follow.
"I think now News International have admitted liability and said that they will pay damages," he told presenter James Naughtie.
"I imagine almost anybody in public life during that period, whether in politics or in showbiz or whatever, will be asking themselves whether it is worth finding out whether their name is on that list, and the technique seems to have been so routine, the chances are very high that anyone in the public glare will find themselves on that list."
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