Comedian Steve Coogan complained neither “the police nor the government” had been willing to hold hackers to account.
Both men were among a list of 19 celebrities and politicians whose hacking damages claims have now been settled.
The development increases the chances the publisher may yet avoid further embarrassing details of its conduct from being publicly aired in court — although at least one of the claimants, singer Charlotte Church, has not yet reached a deal.
A civil trial to establish general principles of how hacking victims should be compensated is due to start next week provided the remaining claimants do not settle.
Gascoigne accepted a £68,000 (€81,000) payout from News of the World publisher News Group Newspapers and Coogan £40,000, Mr Justice Vos was told at a hearing in London.
Lawyers said high-profile figures who also agreed settlements included: Liberal Democrat deputy leader Simon Hughes (£45,000), politician Ge-orge Galloway (£25,000), sports agent Sky Andrew (£75,000) and former Labour communications director Alastair Campbell and Phil Hughes, an agent for George Best, both of whom were awarded “substantial” damages.
Details of the effect hacking had on Gascoigne were given to the judge in a statement prepared by his solicitor, Gerald Shamash.
“[News Group] has recognised that its activities have had a seriously detrimental effect on the well-being of Mr Gascoigne, including mental harm and distress,” said the statement. “[News Group] has apologised.”
The judge was told Gascoigne had been the subject of a number of News of the World articles over many years and had “considerable concerns” about the source of some of the “intrusive and private” information.
“Mr Gascoigne was worried that the information was being obtained by bugging or tapping his telephone conversations, as a result of which he was accused of being paranoid,” said the statement.
“In addition, Mr Gascoigne was worried that the information was being given to the News of the World by his friends of family, as a result of which he fell out with several of his friends and family.”
The judge was told one of Gascoigne’s friends had also been hacked by the News of the World and settled a damages claim.
James Gardner — Gascoigne’s best friend since childhood and referred to in the press as “Jimmy Five Bellies” — had accepted “substantial damages”.
The judge heard Coogan had become “increasingly concerned” about the security of his mobile phone during 2005.
Outside court, Coogan said he was pleased that after “two years of argument and denials”, News International — of which News Group is a subsidiary — “finally agreed to settle”.
“It has been a very stressful and time-consuming experience for me and for those close to me,” Coogan told journalists.
“This has never been about money. Like other people who have sued, I was determined to do my part to show the depths to which the press can sink in pursuit of private information.”
He added: “At the time when these civil cases began, News International seemed likely to succeed in covering up the hacking scandal completely. Neither the police nor the Government were willing to hold those responsible accountable.
“For a long time it was left to victims of these egregious practices to fight for the truth.”