Labour leader Ed Miliband has called for a thorough investigation of alleged "criminal behaviour" at the News of the World.
It comes after News International admitted there were at least eight victims of the phone-hacking scandal.
The company issued an apology and put aside £20m for compensation.
Lawyer Charlotte Harris, involved in several of the current cases, said there would now be a "massive flood of people contacting lawyers".
She told the BBC some of her clients - who include football agent Sky Andrew and actors Leslie Ash and Lee Chapman - had already been contacted by News International and were considering their options.
