The Ay family, who were told that they were to leave the country this morning, were believed to have flown from Stansted airport to Frankfurt at 10.12am.

Human rights lawyer Aamer Anwar, who had lodged an asylum appeal on behalf of the family's four children, said that he had spoken to the Treasury solicitor, who informed him that the children were airborne.

The family had claimed that, if they were sent back to Germany, they would be returned to Turkey, where they feared they would face persecution.

There were no signs of an expected protest at the airport today, despite a high-profile campaign to allow the family to stay in the UK.

The Ays, who had been in the UK for four years, were last week transferred from Dungavel detention centre in Strathaven, Lanarkshire, where they had been held for a year, to a removal centre at Gatwick airport.

The mother, Yurdugal Ay, lost her final appeal to remain in Britain in the House of Lords on Thursday.

Afterwards, Mr Anwar lodged a fresh application for asylum on behalf of the family's four children, who are aged between seven and 14, and then said that the Home Office had refused to consider it.

Scottish Socialist MSP Rosie Kane has taken up the family's case, and has said that she will fly to Berlin to plead with German government officials not to return the family to Turkey.

The Ays have made and lost a series of applications for refugee status in Germany since first arriving there from Turkey in 1988.

After the multiple applications failed, they travelled clandestinely to Britain in a lorry in June 1999.

They faced removal when it was discovered that Germany had already dealt repeatedly with their asylum claim.

The case has caused controversy in the UK. The children are believed to hold the record for the length of time that minors have been held in an immigration detention centre, and their health is said to be suffering as a result.

The family were sent to Dungavel last July, when their mother absconded rather than returning to Germany with her husband, Salih.

He was returned to Germany last March, and the German authorities then returned him to Turkey. The family's lawyers say that he has not been heard from since.

Mr Anwar said that he was in the process of contacting members of the German government, the Green party, Amnesty International and campaign groups.

"The message we are sending to Germany is 'please do not treat the children in the same barbaric fashion that the UK government has'," he said.

Mr Anwar said that the children were issued with a third country certification at the same time as the immigration papers, meaning that they can appeal the decision to deny them asylum from outside the UK.

"We are going to appeal that from Germany on behalf of the children, and we will start work on that today," he said. "Germany continually transfers Kurds to Turkey, and then they disappear."