Calls are mounting for the two British fighters captured in Syria to be sent back to the UK to face trial, with a former counter-terrorism regulator describing it as the “proper forum” for justice.

Lord Carlile, who was the independent reviewer of counter-terrorism laws between 2001 and 2011, intervened as the debate intensified over what happens next to the pair of Islamic State fighters being held by Syrian Kurdish forces.

The fighters, Alexanda Kotey and El Shafee Elsheikh, are the remaining members of “the Beatles”, the British Isis cell that the US State Department has said beheaded a number of western hostages.

Insisting that British courts should deal with radicalised Britons, Carlile said: “They should be returned to their country of origin, where their case should be considered in a normal way with British rights, British duties, British obligations and British responsibilities.”

Granting a fair trial in Britain would, said Carlile, also contribute to domestic deradicalisation. “If people are tried properly, as they would be in the British courts, it would show that the UK is taking a very serious approach to deradicalisation but also to dealing with extremism.”

Carlile also urged that the two fighters should not be sent to Guantánamo Bay, the notorious US prison in Cuba, and said that he hoped the UK government was making sure that this did not happen.

The Liberal Democrat peer and former MP added: “I am totally opposed to anybody being sent to Guantánamo Bay for anything. I would expect the foreign secretary [Boris Johnson] to urge the Americans and the Syrians to accept that British justice is a compliant and efficient system and that the most convenient forum and indeed the proper forum for such cases is the home country.”

His comments echo those of Nicolas Hénin, a French journalist and former Isis captive, who has warned that any attempt to deny the men their civil rights would only help radicalise potential Isis recruits.

Some, including the defence minister, Tobias Ellwood, have argued that Kotey and Elsheikh should be tried at the international criminal court in The Hague, which can prosecute people for war crimes and crimes against humanity.

There is still no confirmation from the US-backed Syrian Democratic Forces – who are holding the two Britons in the north of the country – that they have received a request from any foreign government to hand over the pair. The Home Office on Saturday said it would not comment on whether it would be seeking the pair’s extradition to stand trial in the UK, where both men have family.

Complicating the issue is that the British government has stripped Kotey and Elsheikh of their citizenship to keep them from re-entering the country, effectively making them stateless, although Carlile believes that their “country of origin” should apply in such cases.

Kotey, a father of two from west London, and Elsheikh, a former fairground mechanic, also from west London, were seized last month. They are understood to have been interrogated by the CIA and possibly MI5 and MI6. Officials are seeking information including the whereabouts of the Isis leader, Abu Bakr al-Baghdadi, and John Cantlie, a British journalist held by Isis since 2012.

Meanwhile Amer Deghayes, a 23-year-old anti-Assad fighter from Brighton, who is situated in north-east Syria, has described how Isis fighters have apparently evaded capture by US-backed forces in the east of the country and are starting to move into Idlib, the last rebel-held province.

Deghayes, whose militia have been fighting Isis as well as pro-regime forces, said that Isis sleeper cells had begun attempting to penetrate rebel territory, with one leader caught after planting roadside explosives near the town of al-Tamanah, south Idlib.

He also described how an influx of refugees was putting pressure on resources in the north-east of the country. Anti-aircraft defences were needed, he said, to protect hospitals targeted by Russian and Syrian warplanes over the past week.