Lawyers acting for News International will shock the High Court today when they offer a humiliating apology to victims of phone hacking and announce that Rupert Murdoch's media group has settled dozens of outstanding claims linked to criminal activities at the News Of The World.

There have been months of legal manoeuvring by lawyers acting for the company, which is still aiming to halt a civil trial scheduled for next month and limit the continuing damage to the Murdoch brand. The reputational cost of offering an unqualified apology to dozens of public figures and at least one victim of the worst terrorist atrocity on the British mainland will be balanced by a degree of relief that the company is on the threshold of an endgame for civil claims from the hacking scandal.

News International's senior counsel, Michael Silverleaf, QC, tell Mr Justice Vos at the High Court this morning that 40 of a remaining 50 hacking victims have recently accepted offers to end their legal actions against the Murdoch empire. Among the most high-profile victims who have accepted NI's cash are the Labour MP Chris Bryant and the former footballer Paul Gascoigne.

Others who have settled or are close to settling include: Tony Blair's former communications chief, Alastair Campbell; the disgraced former Labour MP Elliot Morley; and Sheila Henry, whose son Christian Small was killed in the 7/7 bomb attacks on London's transport network.

Lawyers close to the process said the two main law firms engaged in negotiations on behalf of News International, Linklaters and Olswang, were engaged in "a final push" to prevent the civil trial scheduled for 13 February from becoming an arena where more of the NOTW's dirty laundry is seen in public.

Steven Heffer, a solicitor representing the former Labour MP Claire Ward, musician Noel Gallagher's former partner, Meg Mathews, and Dan Lichters, a police officer and former friend of the comedian Michael Barrymore, who were all hacked by the the now-defunct Sunday tabloid, said: "A large number of claims against News Group Newspapers have settled or are close to settlement. These include my clients where agreement has been reached for payment of substantial damages and appropriate apologies, subject to the sanction of judge."

However Mr Heffer said the scale of NI's continuing problems was yet to be fully revealed, adding "There are more claims to come and I am acting for many further victims of phone hacking. The police are informing individuals that they have been victims on a daily basis. They have simply not got round to telling everyone. "