The most notorious member of the group was Mohammed Emwazi, the masked insurgent known as Jihadi John who appeared in several videos that showed the beheading of Western hostages.
Tobias Ellwood, a defence minister whose brother was killed in a 2002 terror attack in Bali, called for the men to be tried by an international war crimes court.
He told the Times: "Given the scale of foreign fighters, we should consider an agreed international process involving The Hague, which ensures terrorists from any origin are transparently and fairly held to account for their actions."
The American-backed Syrian Democratic Forces captured the two men last month.
- AP