The parents of Jack Letts – known as Jihadi Jack – have said the Foreign Office is being "completely obstructive" as they attempt to help their son who is being held by Kurds in Syria.
Mr Letts, who turns 22 today, converted to Islam before travelling to Syria in 2014.
The former Oxford A-level student previously told the BBC he is in solitary confinement in a jail in Kurdish-held north-east Syria.
Mr Letts is charged with being a member of IS but claims he hates the group.
The family also dispute claims their son travelled to Syria to fight alongside IS.
John Letts, Mr Letts father said: "Surely this is illegal.
"In a democratic system in this country, you don't have the death penalty and you can't just go and kill anyone if you think they're guilty."
Sally Lane (55), Mr Letts' mother, told the Guardian the FCO and Boris Johnson have refused to help in getting their son released.
She told the paper: "The Foreign Office have been completely obstructive.
"Alistair Burt (a Foreign Office minister) has sent us four identical letters saying that they can't do anything."
An FCO spokeswoman told the paper: "We have consistently made clear over the last few years that people should not travel to Syria and parts of Iraq.
"As outlined in the FCO's travel advice, the government is unable to provide support to British nationals in Syria as the UK government does not have consular representation there."
Last month, John Letts said he was angered by comments made by international development minister Rory Stewart who said the only way of dealing with British Islamic State fighters in Syria is to kill them in almost every case.