He told Sky News: "They were part of a group of four British jihadis that we nicknamed "The Beatles", as they were, especially at the end of my captivity, responsible for us as a group of about two dozen western hostages".
Despite the fact the cell murdered two Britons - Mr Haines and fellow aid worker Alan Henning, the security source said it was "pretty unlikely" the men would be brought to the UK.
"No punishment is enough for these barbarians and in my opinion they should be sentenced to a slow painful death".
Emwazi - described by IS as an "honourable brother" - appeared in a string of IS videos showing the execution of foreign hostages, starting with the beheading of American James Foley in August 2014.
"Their crimes are beyond imagination", she said.
Foley told the BBC on Friday that the arrests announced Thursday won't bring her son back, but "hopefully it protects others from this kind of crime".
Despite the clear wishes of the bereaved and survivors, it was far from clear what sort of tribunal Kotey, 34, and Elsheikh, 29, who were the last two members of the "Beatles" at large, could eventually face.
Kotey, from west London, was a guard for the execution cell.
Last year, the US State Department said the London-born Kotey had "likely" taken part in executions and used "exceptionally cruel torture methods, including electric shock and waterboarding", while guarding the group's captives.
The alleged ringleader of the group, Mohammed Emwazi, was killed in a drone strike in Raqqa in 2015.
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The US state department says the four-man cell was responsible for beheading several Westerners including US journalists James Foley and Steven Sotloff and American aid worker Peter Kassig.
Both are said to have revealed "valuable information" on the IS leadership and structure.
"I will be extremely frustrated if they were not offered a fair trial and I don't think the local authorities in northern Syria or detention in Guantanamo Bay would be justice".
In January 2017, U.S. authorities named Kotey as a member of the cell and said they had imposed sanctions on him.
In an Associated Press report, Air Force Col. John Thomas, a spokesman for U.S. Central Command, said American officials have been able to interrogate the two detainees. And he characterized their capture as "certainly a big deal for America" as well as the families of the people the two men killed.
The pair are said to have provided valuable intelligence following their capture.
There is some question about what will happen with Elsheikh and Kotey. These men will have been priority targets - but not the only ones. They could be put on trial in the U.S., since they were allegedly involved in the killing of United States hostages - but there may be some in the Trump administration who would like to send them to Guantanamo Bay.
There have been demands for the Government to clarify the status of Kotey and Elsheikh amid claims they remained British citizens.