The father of Josie Russell, who survived a frenzied hammer attack in which her sister and mother were killed, is taking legal action over alleged phone hacking by the News of the World.
Shaun Russell is one of a number of possible victims who have issued legal writs against News International, which owned the former tabloid, sources said.
Sara Payne, the mother of murdered schoolgirl Sarah, is also taking court action over alleged voicemail interception.
She campaigned successfully alongside the newspaper for Sarah's Law, which makes available to parents the addresses of convicted paedophiles.
Princess Diana's former butler Paul Burrell, pop star Dannii Minogue, and 7/7 hero Paul Dadge are also suing Rupert Murdoch's media company, sources said.
Other well-known figures and celebrities claiming damages included politician Lord Prescott, actor Jude Law, comedian Steve Coogan and ex-footballer Paul Gascoigne.
Earlier this year at the High Court, Mr Justice Vos heard that around 30 high-profile people who suspect their phone messages were intercepted by News of the World journalists were taking legal action, but that number is said to have increased to more than 60 in recent weeks.
The Guardian reported the sharp increase is due to a judicial cut-off point for initial claims.
The judge is due to hear evidence from a group of "lead claimants" at a hearing in January - and any rulings he makes are expected to provide a blueprint for the way other claims are dealt with.
A spokesman for News International said on Wednesday: "News International is committed to reaching fair and, where possible, swift settlements with victims of illegal voicemail interception and has unreservedly apologised to those affected."