Police and the Home Office are under growing pressure to answer questions about lapses that allowed Islamic State video suspect Abu Rumaysah to slip through the net.
The jihadi was able to leave Britain for Syria in September 2014 despite being on police bail and having been arrested on six occasions.
Rumaysah's departure has come under the spotlight following claims he was suspected of being a masked militant at the centre of a gruesome film released last week showing the murder of five men accused by IS of spying for the UK.
Police wrote to him politely asking him to call them because he had not surrendered his passport - weeks after he left the country.
The episode also raised questions about Britain's borders, with Rumaysah - born a Hindu called Siddhartha Dhar- departing on a coach from London with his family the day after he was released on bail.
Lord Carlile, the former independent reviewer of terrorism legislation, told the Press Association: "As I commented at the time of Dhar's departure from the UK, the circumstances were a matter of real concern.
"Why had he been granted police bail? Was the CPS consulted? Is there sufficient scrutiny of buses leaving the UK through ferry ports?
"The Home Office should now either release all the relevant documentation so that an open analysis and judgment can be made of what occurred, or appoint an independent person to review the circumstances of Dhar's flight from the UK and report to the Home Secretary."
Rumaysah was arrested in September 2014 - when he was 31 - along with eight other men as part of an investigation into alleged support of the banned extremist group al-Muhajiroun.
However, he left Britain with his family the day after being freed on bail, travelling to Paris and then Syria where he posted a picture of himself on social media, holding his baby son in one hand and an AK-47 assault rifle in the other.
He wrote on Twitter: "What a shoddy security system Britain must have to allow me to breeze through Europe to (IS)."
Following his release on September 26 2014, Rumaysah was given a week to voluntarily surrender his travel documents, which was a condition of his bail.
Yesterday it emerged that a letter from police reminding him of the need to hand over the passport by October 3 was not sent until more than a month later on November 7.
Shadow home secretary Andy Burnham wrote to Home Secretary Theresa May accusing her of "repeatedly" failing to answer his questions in the Commons and calling on her to outline what measures had been taken to prevent a repeat of the lapse.
He wrote: "This is a high-profile individual who was well-known to the authorities, whose disappearance raises serious questions about the robustness of the system."
He also rejected the Home Secretary's claim that figures were not available for cases where terror suspects have absconded.
His remarks followed a statement in which Mrs May said the Government would not comment on the alleged identities of the man or a young boy in the 10-minute film posted online last week.
Reports claim that a boy seen at the end of the video was Isa Dare, the son of jihadi bride Grace "Khadijah" Dare, from Lewisham, south-east London.
The Home Secretary said bail decisions and conditions were an "operational matter" for police.
Since April last year exit checks have been in place on air, sea and rail services while 24 passports were removed from people intending to travel for terrorism-related activity in 2014, she explained.
New powers to temporarily seize the passports of those intending to leave the UK in connection with terrorism-related activity have been used on more than 20 occasions.