The National Council of Resistance of Iran (search) said Abrahim Khodabandeh and Jamil Bassam, members of its foreign affairs committee, had been visiting relatives in Syria when they were arrested on April 18.
On Thursday, the two were "handed over to the Iranian regime in flagrant violation of internationally recognized norms" and now face possible torture and execution, the group said in a statement.
Syrian officials were not immediately available for comment. In London, the Foreign Office said it was aware of the case but could not offer usual consular assistance as the men were not British citizens.
A spokeswoman said the British government took allegations of torture seriously and would investigate the matter with other European Union members.
The council, a Paris-based umbrella group which aims to overthrow the current Islamic government in Tehran and establish democracy, said the men had lived in Britain for some 30 years and called on the British government to intervene.