Baghdad has been the scene of recent violence
Around 30 failed asylum seekers remain in UK detention after being refused re-entry to Iraq when their deportation flight landed in Baghdad.
Only 10 refugees were admitted by Iraqi authorities on Thursday.
The UK Border Agency says it will send another flight but has not revealed when. One detainee told the BBC he was "very, very scared" for his future.
Meanwhile, campaigners opposed to deportation to Iraq on safety grounds have demonstrated in Parliament Square.
Richard Little, of the International Federation of Iraqi Refugees, said: "These people are very, very unhappy and don't want to go back."
Twelve MPs have signed an early day motion laid down by John McDonnell, MP for Hayes and Harlington in west London, calling for the flights to be halted.
The motion, which will not be debated but is used to draw attention to an issue, criticises "the deportation of innocent people to face violence, hardship and even death in a war zone like Iraq".
Salam Hussein, 34, was among the detainees who were refused entry to Iraq.
He claims he was handcuffed during the flights to and from Iraq and made other allegations about the way they were treated during the journeys.
It is understood that about 80 escorts were aboard the government-chartered flight.
Hussein told the BBC - via a friend who was interpreting - that when they arrived at Baghdad airport, an Iraqi official told UK immigration officers: "Don't send these guys again, we won't take them back."
The detainee said he fled his native Iraq for the UK in 2002, after his Shia family were murdered.
His asylum claim was rejected and he was eventually earmarked for deportation this year, having served six months in jail for using false identification to get a job as a cleaner.
Hussein fears he will be kidnapped or killed if he returns to Iraq.
"I'm very, very scared. I can't sleep properly and I don't know what's going on," he said.
Reports have suggested Iraq's authorities were not happy they could confirm the identities - or even nationalities - of the deportees.
Government spokesman Ali al-Dabbagh suggested some of the men may have falsely claimed to be Iraqi on arrival in the UK in order to help their asylum claims, according to the AFP news agency.
The Home Office has said the reason the detainees were sent back to the UK is "a matter for the Iraqi government", while the UK Border Agency has pledged to "iron out" any problems to allow another flight to leave shortly.
There have been no returns to Iraq since 2008 and this was the first attempted return to the capital city since the start of the Iraq war in 2003.