The 10 are thought to have left Britain at 5.15am on Wednesday on a chartered flight which was scheduled to stop in Sweden to pick up more Iraqi detainees before heading to Baghdad.
The planned deportation had provoked a storm of criticism from campaigners and the UN High Commissioner for Refugees, who said the Iraqis could be killed if they were sent back.
Spokesman Peter Kessler made a last-ditch plea for mercy, saying: "We are asking the government to continue hosting people from central Iraq until such a time that they can be returned in safety.
"The situation in central Iraq is very unstable due to the prevailing violence, security incidents and human rights violations going on. Their lives could be at risk."
But to make sure the flight was not "disrupted or delayed," the Treasury Solicitor's Department had already written to the High Court on June 2 requesting that judges refuse to consider last-minute judicial review applications by detainees due for deportation.
The department's Andrea McMahon wrote: "Because of the complexities, practicalities and costs involved in arranging charter flights, it is essential that these removals are not disrupted or delayed by large numbers of last-minute claims."
She said only a full-scale injunction would block the flight.
"It is an extraordinary interference by the executive in the judicial process," said immigration law expert Frances Webber.
"Coming hard on the heels of the letter requesting judges to withdraw their criticism of MI5, it seems the government's lawyers have not learned the lesson of that case."
The Stop Deportation Network added: "It is incredible the government would go as far as telling judges not to do their job."
Another flight with 40 deportees from Britain is due to leave next Wednesday.
The first deportation flight of Iraqis last October was disrupted by last-minute judicial reviews that forced the government to substitute others held in detention. It is thought these special measures are being put forward to prevent a recurrence.
In the end 34 of the 44 deportees were sent back by Iraq because they were Kurdish.
Source: Morning Star