The publisher of the Daily Mirror and Sunday Mirror is to pay compensation to 10 victims of phone hacking, including former England manager Sven-Göran Eriksson and one-time Doctor Who actor Christopher Eccleston.

It is the first significant admission of phone hacking by a newspaper group not owned by Rupert Murdoch, and was described as significant because it confirms that the practice was widespread in parts of the British newspaper industry.

Trinity Mirror is understood to have set aside just under £10m to cover the costs of dealing with claims of phone hacking, a sum that includes the £4m settlement fund announced in July this year.

Mark Lewis, the lawyer who acted for clients including Eriksson, said: “There are many more people who will now be able to make claims against the Mirror Group titles in respect of their unlawful activities.”

Lewis is the lawyer who also brought the first successful phone-hacking legal claim against Rupert Murdoch’s now-defunct News of the World.

The claims are understood to be directed at all three national newspapers owned by Trinity Mirror, which also owns the People as well as the Daily and Sunday Mirror. The claims are concentrated in the five years between 2000 and 2005, when the Daily and Sunday Mirror and Sunday People were edited by several different people.

Eriksson’s claim was filed in October 2012 and is understood to relate to a time when Piers Morgan edited the Daily Mirror, between 1995 and 2004. Morgan has denied any knowledge of phone hacking.

Trinity Mirror admitted liability to four individuals: Alan Yentob, the BBC’s creative director, EastEnders stars Shane Richie and Lucy Benjamin, and Coronation Street actor Shobna Gulati. All received apologies and unspecified sums in compensation.

The newspaper publisher has also settled six other alleged phone-hacking claims and has agreed compensation. These claimants are ex-footballer Garry Flitcroft, Richie’s wife, Christie Roche, and his agent, Phil Dale, and Abbie Gibson, a former nanny for the Beckham family, as well as Eriksson and Eccleston.

There are 19 more individuals who have issued hacking claims against Trinity Mirror, with a further 10 known to be considering further action.

Evan Harris, the associate director of Hacked Off, the campaign for tighter press regulation, called the admission “just the tip of a very big iceberg” and said that he believed the situation was “very worrying for the future of the paper. [The Mirror] is the only leftwing paper left and it doesn’t have the deep pockets of Rupert Murdoch.”

Morgan gave evidence to the Leveson inquiry in December when he repeatedly denied any knowledge of illegal newsgathering techniques at the tabloid. But in May BBC Newsnight presenter Jeremy Paxman claimed to the inquiry that Morgan had personally shown him how to illicitly intercept voicemail messages at a lunch in September 2002.

Paxman claimed that at the same lunch Morgan had teased Ulrika Jonsson about the details of a private conversation she had had with Eriksson, who was England manager at the time.

Flitcroft was granted an injunction against the Sunday People in 2001, which was lifted in 2002. He subsequently told the Leveson inquiry that he had been subjected to a “dirt-digging” exercise in which details of his private life were published. Lucy Benjamin has cited 11 instances of alleged hacking against all three tabloid titles for a period covering 2000-2005.

Trinity Mirror has previously defended itself against allegations of phone hacking at its titles. In January 2012 Sly Bailey, the former chief executive, explained why there had been no internal investigation to the Leveson inquiry by saying: “I don’t think it’s a way to conduct a healthy organisation to go around conducting investigations when there’s no evidence that our journalists have been involved in phone hacking.

“There was no evidence and we saw no reason to investigate. We have only seen unsubstantiated allegations and I have seen no evidence that phone hacking has ever taken place at Trinity Mirror.”

Lewis said such denials were initially repeated by the company’s current management. “Their new chief executive, Simon Fox, indicated that a full internal investigation had been made and there was no substance in the allegations. This was completely wrong.

“It has finally come out that Mirror group journalists included people who did not follow the PCC code and the paper’s denials in the past have been false. There are many more people who will now be able to make claims against the Mirror group titles in respect of their unlawful activities.”

Harris also cited evidence in the recent phone-hacking trial that saw former News of the World editor Andy Coulson found guilty. During the trial Dan Evans, a former reporter at the Murdoch tabloid, gave evidence. Evans was given a suspended sentence in recognition of his co-operation with police and prosecutors, having admitted hacking phones while he worked at the News of the World and his previous employer, the Sunday Mirror.

Evans had admitted in court in January that he started hacking phones after he was made a staff reporter at the Sunday Mirror and carried out this activity at that title for about “a year and a half”.

Evans described the phone-hacking target list at the Sunday Mirror as containing “lists of celebrities’ voicemail pin numbers” and “celebrity agents’ [voicemail numbers] where you would pick up voicemails left by them”.

He admitted hacking the voicemails of 200 people and listening to about 1,000 voicemails in total.

In a statement, Trinity Mirror “admitted liability to four individuals who had sued MGN for alleged interception of their voicemails many years ago”, before adding: “MGN has apologised to those individuals and agreed to pay compensation. The amount of that compensation will be assessed by the court if it cannot be agreed.”

The original allegations of phone hacking at the News of the World eventually led to a large-scale police investigation that uncovered many victims and led to the newspaper’s closure, as well as the trial of some former executives. It also prompted the Leveson inquiry into press standards and regulation.