Actor David Tennant is suing the owners of the defunct News of the World over alleged phone hacking.
His lawyers issued a claim for compensation at the High Court in London on Thursday.
Law firm Collyer Bristow said it was representing nine people in total, including former Formula One driver Eddie Irvine. They said other law firms have also issued claims this week.
News UK, which owned the paper until it closed in 2011, declined to comment.
Collyer Bristow said its clients had been left with “no alternative” following the closure of a compensation scheme.
It said the News of the World had previously “admitted and apologised for hacking into the voicemails of a number of high-profile individuals” and opened a compensation scheme in 2011 as an alternative to litigation.
But Collyer Bristow said the scheme closed “after less than 18 months of operation”.
The NoW was shut down by owner Rupert Murdoch following the revelation that the phone of murdered schoolgirl Milly Dowler had been hacked.
The scandal also led to the establishment of the Leveson Inquiry into press ethics, an MPs’ inquiry and the launch of three police investigations into alleged widespread phone hacking and corruption.
Former News of the World editor Andy Coulson – who later became director of communications for then Prime Minister David Cameron – was jailed for 18 months for conspiracy to hack phones.
Steven Heffer, who is acting on behalf of the claimants, said: “My firm continues to act for a number of clients with claims against News Group arising out of phone hacking and other unlawful activities.
“News Group withdrew its compensation scheme in 2013, giving no proper explanation for this move and has failed to compensate victims despite all attempts by lawyers to settle cases out of court.”
The firm says it has now acted for more than 200 “victims of hacking and unlawful surveillance”.
Collyer Bristow said other claimants included Fran Cutler, Jess Morris, Tanya Frayne, Sophia Myles and Rob Gros.