Four British newspapers have paid substantial damages to the parents of missing toddler Madeleine McCann, after settling a libel case over reports which suggested the couple were involved in their daughter's disappearance.

Kate and Glasgow-born Gerry McCann accepted £550,000 libel damages over the allegations.

The couple, who were not at London's High Court for the hearing, said they were pleased Express Newspapers had admitted the "utter falsity" of the articles.

As well as the damages, the couple also accepted a public apology.

Their solicitor-advocate, Adam Tudor, told Mr Justice Eady that from the late summer of last year until February this year, the Daily Express, the Sunday Express, the Daily Star and the Daily Star Sunday, which have a combined circulation of several million copies as well as a substantial online readership, published more than 100 articles which were seriously defamatory of the couple.

He said: "The general theme of the articles was to suggest that Mr and Mrs McCann were responsible for the death of Madeleine or that there were strong or reasonable grounds for so suspecting and that they had then disposed of her body; and that they had then conspired to cover up their actions, including by creating 'diversions' to divert the police's attention away from evidence which would expose their guilt.

"Many of these articles were published on the front pages of the newspapers and on their websites, accompanied by sensational headlines.

"In addition to the allegations referred to above, the Daily Star published further articles (under the headlines 'Maddie mum 'sold' her' and 'Maddie 'sold' by hard-up McCanns') which sought to allege that Mr and Mrs McCann had sold their daughter in order to ease their financial burdens.

"A further article alleged that Mr and Mrs McCann were involved in 'swinging' or wife-swapping orgies."

Mr Tudor said the all the libel damages would be donated to the fund established to assist with the search for the youngster, who disappeared from Praia da Luz, Portugal, in May last year on the day before her fourth birthday.

The Daily Express and Daily Star ran prominent pieces at the top of their front pages today, headlined "Kate and Gerry McCann: Sorry".

The McCann's lawyers complained several weeks ago over the articles, which appeared after Portuguese detectives last September named the couple as "arguidos", or official suspects, in their daughter's disappearance.

The McCanns are reserving the right to sue other papers for libel.

Last August they launched a defamation action against the Portuguese newspaper Tal & Qual over a front-page story which claimed police believed they killed their daughter.

The August 24 article alleged the Policia Judiciaria (PJ) - Portugal's CID - were certain the couple accidentally caused Madeleine's death.

It is understood that Tal & Qual has since folded.

Madeleine, of Rothley, Leicestershire, went missing, in Praia da Luz in the Algarve on May 3 last year. A police investigation and international hunt for the girl continues.

The Daily Express's front-page apology, run under the headline "Kate and Gerry McCann: Sorry", says it has taken the "unprecedented step" of making a front-page apology to the McCanns.

"We do so because we accept a number of articles in the newspaper have suggested the couple caused the death of their missing daughter Madeleine and then covered it up.

"We acknowledge there's no evidence whatsoever to support this theory and that Kate and Gerry are completely innocent of any involvement in their daughter's disappearance. We trust that the suspicion that has clouded their lives for many months will soon be lifted.

"As an expression of its regret, the Daily Express has now paid a very substantial sum into the Madeleine Fund and we promise to do all in our power to help efforts to find her.

"Kate and Gerry, we are truly sorry to have added to your distress. We assure you that we hope that Madeleine will one day be found alive."

The Daily Star said it had made a "substantial donation" to the fund in a "wholehearted" apology which followed a similar vein to the Express's.

The Star accepted stories suggesting the couple "were responsible for or may be responsible for the death of their daughter Madeleine and for covering it up" were "absolutely untrue and that Kate and Gerry are completely innocent of any involvement in their daughter's disappearance."

The Sunday Express and Daily Star Sunday are expected to carry similar full apologies in their next editions.

Speaking to The Herald last night, Madeleine's grandmother from Glasgow, Eileen McCann welcomed the settlement and called for the media to lay off the couple.

She said: "We don't like reading anything derogatory about Gerry and Kate for the simple reason that they have gone through enough, without making it worse. They have lost a little child and it is just hard going for them having to deal with this."

Media commentator Roy Greenslade said that for two national newspapers to carry front-page apologies at the same time was an "unprecedented climbdown".

The fact that the papers capitulated without a fight suggested that their legal advisers told them they had no chance of winning if the case went to trial, he said.

"This was no journalistic accident, but a sustained campaign of vitriol against a grief-stricken family. The stories were not merely speculative, but laced with innuendo which continually made accusations against the McCanns on the basis of anonymous sources and without any hard evidence." he said.

"Wild claims, often made by unattributed sources to Portuguese newspapers, were then spun even more negatively by the Express and Star titles."