An worldwide manhunt for the fighters began in August 2014 when ISIS released a video of Foley's execution at the hands of an English-speaking militant, who called himself "John.' Foley's executioner and leader of the cell was dubbed 'Jihadi John" by the British press.
It was announced on Thursday that the two remaining members of the cell had been captured by Syrian Kurdish forces.
She later told BBC Scotland that she personally would have wanted the men to die a "slow, painful death".
"Their crimes are beyond imagination". "I didn't know what to feel, I didn't know what to think and then you kind of realise it's real and you think that's it, they're gone, they can't hurt anyone else".
They are believed to be linked to the British terrorist known as Jihadi John, the masked IS militant who appeared in several videos depicting the graphic beheadings of Western hostages.
Ms Haines said she would like them to be "locked up with the key thrown away" and is hopeful their capture will bring closure to bereaved families. They should never be allowed back in society because they will just recruit people and they will do this again. "What I want is a trial and a trial potentially that I can attend, so rather, a trial in London rather than one in Kobani in northern Syria".
She said: "I got a call to say that they had been captured. Hopefully there will be some justice".
US officials have interrogated the men, who were part of the IS cell that captured, tortured and beheaded more than two dozen hostages, including American journalists James Foley and Steven Sotloff and American aid worker Peter Kassig.
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"It's hugely significant for a lot of the Western countries who had hostages who were captured by Islamic State", he said.
Asked if they would be prosecuted and if so where they might face trial Major Adrian Rankine-Galloway said: "We are still considering options regarding el-Sheikh and Kotey, but rest assured our intention is to hold anyone accountable who commits acts like those they are alleged to have committed".
"Jihadi John" was seen in ISIS videos which showed the beheadings of journalists James Foley and Steven Sotloff, British aid workers David Haines and Allan Henning, and Japanese hostage Kenji Goto. US officials sought to keep their capture under the radar to give more time to prepare raids against ISIS targets and follow-up on intelligence leads.
Sources told the broadsheet that there was little desire among ministers to repatriate them to Britain.
Kotey, 34, and Elsheikh, 29, were the last two members of the group to remain at large.
The capture of the last two members of the "Beatles", who are thought responsible for murdering 27 hostages, has been independently confirmed by the Guardian and the Reuters news agency. The fourth man, Aine Davis, is reportedly in a Turkish prison on accusations of terrorism.
He was staying with other aid workers in Atmeh when he was kidnapped alongside Italian colleague Federico Motka, who was later released.
His postings for worldwide aid agencies took him to some of the most unsafe places in the world, and was said by his family to have "helped whoever needed help, regardless of race, creed or religion".