The Daily Mirror, Sunday Mirror and The People, all part of Mirror Group Newspapers (MGN) face allegations that staff hacked the voicemails of four high profile figures, including ex-England manager Sven Goran-Eriksson.
The scandal mirrors those made against News Corporation last year that led to the eventual closure of the News of The World.
Trinity Mirror, the parent company of MGN, responded by saying: "All our journalists work within the criminal law." It added that it had not yet received any claims or evidence.
Media laywer Mark Lewis, who also brought claims against News International, lodged the claims on Monday, the same day that a management overhaul at Trinity Mirror was announced.
A new management team, headed by recently appointed chief executive Simon Fox, were welcomed with soaring shares of 72.5p on Monday. This plummeted to a 62p trough on Tuesday as the hacking allegations emerged in the press.
As part of its 'One Trinity Mirror' strategy to merge its national and regional papers, Daily Mirror editor Lloyd Embley was promoted to editor-in-chief of the national titles. Paula Scott will become publishing director of the same portfolio.
Three rejigged publishing regions were announced to unify the national and regional publications.
North West, covering Manchester, Liverpool and North Wales will be led by Steve Anderson-Dixon, brought over from Northcliffe publishing.
Simon Edgley, previously managing director of Trinity Mirror Southern, will oversee the Midlands & South region. This area will look after Birmingham, South Wales and southern markets, while Media Scotland will be paired with Middlesborough and Newcastle under the Scotland & North East England branch.
Denise West will become Scotland & North East’s managing director and MGN Ireland will be headed by Joanne McGreevy.
Director of advertising David Emin is promoted to managing director of Trinity Mirror National Sales. He will oversee the sales and marketing unit representing regional, national and digital brands.
The unified unit will include AMRA, Trinity Mirror’s advertising sales business, still headed by Gary McNish.
Trinity Mirror Digital Media’s new managing director Ian Dowds will aid Emin in driving digital revenues.
Chief operating officer Mark Hollinshead, who was recently promoted with chief executive Fox, said: "The unified management structure for One Trinity Mirror will ensure that we have the best team in place, in the right markets, to help us achieve our ambitions to grow revenues, and accelerate our plans for all our digital and newspaper brands.
"We have in place a more cohesive publishing structure that brings editorial to the heart of the decision making process. This move will ultimately benefit our journalism, our readers and our advertisers."
Trinity Mirror's share prices returned to 64p as trading opened this morning.