Boris Johnson has said he wants the reportedly English jihadist who beheaded an American journalist to be killed in a bomb attack and has joined the growing calls for Britons fighting abroad to be stripped of their citizenship.
The Mayor of London said Britain must take on Islamic State (IS) and "try to close it down now", warning that doing nothing would mean a "tide of terror will eventually lap at our own front door".
Mr Johnson, who has overall responsibility for the Metropolitan Police, called for new laws that would mean anyone visiting Iraq and Syria would be automatically presumed to be terrorists unless they had notified the authorities in advance.
British intelligence agencies are close to identifying the IS (formerly ISIL) brutal killer who has been dubbed "jihadi John".
Writing in his Daily Telegraph column, Mr Johnson said: " Young men such as this killer are famously told that if they die in 'battle' they will be welcomed in heaven by the sexual ministrations of 72 virgins.
"Many of them believe it - even though scholars have suggested that the reference to 'black-eyed virgins' is in fact a promise of 72 raisins. I suspect most of us don't give a monkey's what happens to this prat in heaven, whether he meets virgins or raisins - we just want someone to come along with a bunker buster and effect an introduction as fast as possible."
Former shadow home secretary David Davis has called for IS fighters to lose their British citizenship and Lord Carey, former Archbishop of Canterbury, said they must face being stripped of their passports.
Mr Johnson said those who "continue to give allegiance to a terrorist state" should lose their British status citizenship and called for swift changes to the law so there is a "rebuttable presumption" that those visiting war areas without notifying the authorities have done so for a terrorist purpose.
The mayor said that while Britain's recent military interventions have left the nation reluctant to wade into overseas conflicts " doing nothing is surely the worst of all" and warned that the IS "wackos" must be tackled.
" What is the point of having a defence budget, if we don't at least try to prevent the establishment of a terrorist 'caliphate' that is profoundly hostile to civilised values?"
Britain's ambassador to the United States Sir Peter Westmacott confirmed that intelligence agencies are on the brink of identifying the IS terrorist.
He told CNN's State of the Union programme: " I do know from my colleagues at home that we are close.
" We're putting a lot into it. And there are some very sophisticated technologies, voice identification and so on, which people can use to check who these people are. But, of course, the problem goes beyond one horrendous criminal, if you like."
Foreign Office and Home Office officials refused to comment on the claims.
"We do not comment on security matters," a Foreign Office spokesman said.
Downing Street said the Government was "stepping up" efforts to defeat IS terrorists and announced that Lieutenant General Sir Simon Mayall has been appointed as security envoy to the Kurdistan region of Iraq.
Body armour, night vision goggles and other non-lethal equipment will be supplied to Kurdish forces over the next few days.