Trinity Mirror has increased its provision for dealing with phone-hacking damages claims to £41m.
This increase, from £28m, comes after the Court of Appeal rejected its appeal against the £1.2m in damages awarded to eight victims of phone-hacking in May.
The judgment said the publisher should not "expect this court to come to its rescue and find some way of finding the awards to be excessive".
Trinity Mirror responded by saying it has increased its provision for dealing with hacking claims by £13m. After the initial judgment, this provision was increased from £12m to £28m.
A lawyer acting for the claimants revealed today that there are "currently 80 other claims before the court in the second wave of this litigation and at least 50 further claims at the pre-action stage".
Press Gazette understands 28 individuals made up the first wave of claims. This means that at least 158 individuals have either sued Trinity Mirror over hacking in court or are at the pre-action stage.
However, the company intends to take the case to the Supreme Court, saying: "We continue to believe that the basis used for calculating damages is incorrect."
The Court of Appeal judgment comes less than a week after Trinity Mirror and its journalists were told they would not face any criminal phone-hacking charges by the Crown Prosecution Service.
Mr Justice Mann's ruling in May saw the payment of record compensation as a result of the invasions of privacy concerned being "so serious and so prolonged".
All of the awards exceeded the previous highest sum given by a UK court in a privacy case – the £60,000 won by former Formula 1 boss Max Mosley, who successfully sued the now defunct News of the World in 2008 – and are expected to provide a framework for resolving similar civil actions in the pipeline.
Actress and businesswoman Sadie Frost received the largest sum of £260,250, with ex-England footballer Paul Gascoigne getting £188,250.
The other payments were £85,000 to TV executive Alan Yentob, £117,500 and £157,250 respectively to actresses Shobna Gulati and Lucy Taggart, and £155,000 to soap star Shane Richie.
TV producer Robert Ashworth, who was married to actress Tracy Shaw, received £201,250, and flight attendant Lauren Alcorn, who had a relationship with footballer Rio Ferdinand, was awarded £72,500.
Explaining why the damages were so large, in his original judgment Mr Justice Mann said: “The fact that they are greater than any other publicly available award results from the fact that the invasions of privacy involved were so serious and so prolonged.”
For example, Yentob’s phone was targeted from 1999 to 2006 at least twice a day, and often several times a day.
In a statement after the ruling, Trinity Mirror said: "We continue to believe that the basis used for calculating damages is incorrect and we therefore intend to appeal this matter to the Supreme Court.
"As a consequence of this decision and the continued uncertainty as to how matters will progress we are increasing our provision to deal with these matters by £13 million.
"The Board remains confident that the exposures arising from these historic events are manageable and do not undermine the delivery of the Group's strategy."
Dismissing the appeal, Lady Justice Arden said: "MGN has asked the court to reduce the awards without, as the respondents point out, taking the court to so much as a single award which they contend is excessive or explaining the element of it which is on their case excessive.
"I have, as it happens, read the articles alongside the judge's detailed rulings on them. It does not strike me reading them, in the light of the judge's rulings and his factual findings, that any of them involved an error of law.
"The test is not whether I would have made exactly that award – the assessment of general damages is not an exact science – but whether he was entitled to make the awards that he did.
"MGN cannot expect this court to come to its rescue and find some way of finding the awards to be excessive when its staff have been responsible for disgraceful conduct with such distressing consequences, and when to boot it is quite unable itself to point to actual awards that it contends are wrong.
"These appeals, hopefully, concern an exceptional situation. There were misuses of private information beyond our ability to know and count.
"So it is wrong to look at the global sums in the schedule which each respondent has been awarded without remembering that fact.
She added that as far as she could see, there were no mitigating circumstances.
"The employees of MGN instead repeatedly engaged in disgraceful actions and ransacked the respondents' voicemail to produce in many cases demeaning articles about wholly innocent members of the public in order to create stories for MGN's newspapers.
"They appear to have been totally uncaring about the real distress and damage to relationships caused by their callous actions.
"There are numerous examples in the articles of the disclosure of private medical information, attendance at rehabilitation clinics, domestic violence, emotional calls to partners, details of plans for meeting friends and partners, finances and details of confidential employment negotiations, which the judge found could not have been made if the information had not been obtained by hacking or some other wrongful means.
"The disclosures were strikingly distressing to the respondents involved."
James Heath, of Atkins Thomson, which represented the claimants in the litigation, said: "It has taken great courage for this group of eight individuals to hold their nerve and persevere against the largest newspaper publisher in this country.
"In doing so, they have achieved guidance that will allow many more people to be fairly compensated for similar abuse carried out against them by the tabloid press.
"There are currently 80 other claims before the court in the second wave of this litigation and at least 50 further claims at the pre-action stage.
"They will all be assisted by the trial decision achieved by these eight claimants and the guidance given by the Court of Appeal."
A Trinity Mirror spokesperson said: “We are disappointed that the original judgment in the civil trial for the assessment of damages related to phone hacking has been upheld. We continue to believe that that the basis used for calculating damages is incorrect and the amounts awarded are excessive and disproportionate, far beyond what could be expected in cases of serious physical injury or mental suffering.
"We are keen to move the process forwards and settle outstanding claims at appropriate levels but still hold the view that there are hugely important principles at stake for the wider media industry and law of the UK, and so we will be appealing to the Supreme Court.”