Three young girls are thought to have been put on a plane to Pakistan without an accompanying adult after their parents became afraid that they would be taken into care, the High Court has heard.
Alyssa Din, 15, and her sisters Safia, five, and Amani, then three but now four, flew to Karachi via Islamabad in October after leaving their home in Preston, Lancashire - and their whereabouts remain unknown, a judge was told.
Mr Justice Hayden described the missing girls' ordeal as "alarming", "brutal" and "almost impossible to imagine".
Details emerged at a hearing in the Family Division of the High Court, as the judge ruled that the identities of the children and their parents could be revealed in the hope that publicity might lead to the youngsters being found.
Sources close to the case said the girls had flown from Heathrow. A spokeswoman for the airport said today: "We can't comment."
Mr Justice Hayden said the girls' father, Ilyas Din, and mother, Mazeley Din, are in prison for contempt of court after failing to provide information about the children's whereabouts.
Mr Din, who is in his late 40s, was given a 12-month term and Mrs Din, who is in her 30s, a six-month sentence.
The couple, who have other children and have been together for 17 years, were jailed following a hearing in Liverpool in December.
Mr Justice Hayden had decided at that stage not to reveal the family's identities because he thought publicity might harm any children still in England.
But at the latest hearing, in London yesterday, he said he had changed his mind - concluding that the balance had been tipped in favour of the media's right to "freedom of expression".
Following the December hearing, Mr Justice Hayden published a written ruling.
"What is clear in this case is that, on the 7th and 8th of October, three of the children were flown out to Pakistan," he said.
"There has been much discussion about how those children came to be put on that plane in that alarming and, in my view, quite brutal manner.
"What seems likely, doing the best I can on the evidence available to me, is that they were put on the plane without any adult to accompany them. The burden for looking after the two younger ones appears to have been placed on the 15-year-old.
"The children's final destination was Karachi. That took them by Islamabad. One cannot begin to imagine the anxiety that that trip must have caused to those children.
"It is not difficult for any adult member of the public to understand why, when a family feels the local authority to be circling in, they might panic and run away together to evade the consequences of intervention. I do not for a moment condone that, of course. But I do understand it.
"What is far more difficult to understand is the parents who would put a three-year-old on a plane to an alien continent in this way. They must both have become very removed from their children's most basic emotional needs."
He added yesterday's hearing: "It is almost impossible to imagine how traumatic this experience will have been to these children."
The couple appeared at the hearing yesterday via video-links from jail.
"What am I supposed to do?" Mrs Din asked the court.
"I am trying to get my children back but nobody is helping me get my children back. You have just put me in prison."
Mr Din apologised, and said he had been in contact with a relative in Pakistan and hoped that the three children would soon be returned to England.
"There has been a mistake down to our panic," Mr Din told the judge. "We are loving parents but we were afraid because we were threatened by social workers."
He added: "We are not bad people. We just made a mistake. People do make mistakes. We do apologise."
A lawyer representing Lancashire County Council's social services department told the judge that the local authority had been "simply seeking to make inquiries regarding the children's welfare".
She said there had been no application to remove the children "prior to the parents' actions".
A Heathrow spokeswoman said today: "Unfortunately we can't comment on individual cases but parents can book children as unaccompanied minors with an airline and the airline's staff would then escort them through security."
She could not say whether Heathrow had carried out an internal inquiry.
Mr Justice Hayden told yesterday's hearing that the "mother's will had been subjugated by the father".
And he outlined some of the background to the case.
The judge said people had been "so concerned" about the "noise of violence" coming from the Din home that they had twice called police.
He said Mr Din had stood trial accused of causing grievous bodily harm to Mrs Din but had been acquitted after Mrs Din told jurors that there had been a "terrible accident".
Prior to the judge entering court for the hearing yesterday, Mr Din could be heard speaking via the video-link.
He said: "You are going to witness some crazy stuff going on in this court... in the name of our great nation, England."