Lord Carey says those who leave Britain's shores to engage in terrorism should not be allowed to return.
The former Archbishop of Canterbury writes in the Daily Mail that Britons who are fighting for foreign terrorist groups, and any planning to travel overseas to commit terrorist acts should have their passports withdrawn.
He said it would take a "brave" government to carry this out but said it was his feeling that the majority of Britons would support such a measure "out of sheer disgust" that fellow Britons are "killing others in the name of Islam and so challenging the tolerant values that stem from our Christian heritage".
"They should not have access to the privilege of travelling under a British passport with the accompanying consular protection – and they certainly should not be able to travel back to their shores with the barbaric and bloodthirsty skills they have gained," he said.
"Young people who travel abroad to commit violent 'jihad' should know before they go that there is no way back to civilised society.
"It may focus their minds to know that the privileges and luxuries of our country (including our gyms, games consoles and relative peacefulness) will be denied to them in future."
Lord Carey was writing after the militant who was filmed executing American journalist James Foley appeared to be British.
The Govenment is urgently trying to identify the militant - known as Jihadist John - as British Foreign Secretary Philip Hammond warned that "sooner or later [the Islamic State] will seek to strike us on British soil" unless they are stopped.
Writing in the Sunday Times, Mr Hammond said the security and intelligence agencies estimate that more than 500 British jihadists have travelled to Syria or Iraq in the past few years.
He said passports are being removed from those supsected of planning to travel to commit terrorist activies abroad.
"The likely involvement of a British citizen in last week's horrific beheading is further proof of the threats we face from individuals who may carry our passport but do not share our values," he said.
"It is horrifying to think that the perpetrator of this heinous act could have been brought up in Britain. It is an utter betrayal of our country, our values and everything the British people stand for."
Shadow Home Secretary Yvette Cooper added: "This is no Spanish civil war. Isil extremists are beheading people and parading their heads on spikes, subjugating women and girls, killing Muslims, Christians and anyone who gets in their way.
"This is no liberation movement — only a perverted, oppressive ideology that bears no relation to Islam."