The UK government was under pressure to rethink its approach to tackling domestic extremism as security services, led by MI5, intensified the search for a masked jihadi, suspected of being a British citizen, who is believed to have beheaded US journalist James Foley in Syria.

As Foley's employers revealed that the terror group Islamic State (Isis) demanded a ransom of $132m (£80m), MPs on both sides of the House of Commons called for a step change in the fight against extremist groups amid fears that up to 300 British citizens are fighting with Isis.

The US justice department opened a criminal investigation into the killing, while a French journalist who was held hostage alongside Foley in Syria confirmed that he "roughly" knew the man, a suspected hostage guard known as "John". Didier François, 53, who was freed in April, told Europe 1 radio: "Recognised is a very big word. I see roughly who it is."

British Ggovernment sources, meanwhile, suggested that the British jihadi featured in the video may not have been the killer. A detailed examination of the video showed it was composed from different frames and that "John" may have appeared because Isis propagandists wanted to spread their message with a British accent. One government source said that the actual killer may have been a different fighter.

One intelligence source described the video as a "polished propaganda piece", put together and composed from different frames. The body language did not suggest that the killing took place in the way, and with the weapon, that the video suggested, sources said.

They also said describing the operation as a "hunt" is misleading since the individual in the video – believed to be a Briton who called himself "John" – was unlikely ever to be extradited or brought to justice. However, his identity could be confirmed in a variety of ways – in a Twitter message, for example, or from an old friend, sources said.

The race to identify the jihadi in the video came as the government faced growing pressure to change tack in the fight against extremism in Britain on a series of fronts.

Julian Lewis, a member of parliament's intelligence and security committee (ISC), which is due to publish a report into the murder of the British soldier Lee Rigby in the autumn, called for the government's anti-extremism strategy to be widened beyond confronting advocates of extremist violence to tackling promoters of extremist ideology. In an echo of Michael Gove's call for a "draining of the swamp", Lewis told the Guardian: "If we try to be neutral between the arsonist and the fire brigade then we run into problems. We were not neutral in this country between Nazi doctrine and democracy or between Communist doctrine and democracy. We should not be neutral between Islamist totalitarianism and democracy." Lewis declined to comment on the ISC report into the murder of Rigby line with the committee's procedures.

In a sign of growing concerns about the challenge of monitoring terror suspects, the former Middle East minister Alistair Burt led a cross-party call for a debate about reintroducing control orders which were criticised for allowing indefinite house arrest. Burt, who was a minister when the control orders were scrapped in 2011 and replaced with terrorism prevention and investigation measures (TPims), told the Guardian: "If the authorities believe someone to be dangerous – what sort of monitoring is possible of that individual? That raises the issue of control orders coming back onto the agenda again. It is time to revisit control orders. These were cancelled when we came into office. But circumstances have changed."

The debate about the battle against domestic extremists will be thrown into sharp relief in the autumn when parliament's security and intelligence committee publishes its report into the killing of Rigby who was murdered in a similarly brutal fashion to Foley in Woolwich, south-east London.

The report will confirm that Rigby's murderers, Michael Adebolajo and Michael Adebowale, were known to MI5. The report is not expected to criticise MI5 for failing to recognise the threat they posed. It is instead expected to say that a debate needs to be held about whether the intelligence agencies need to reinforce their powers of surveillance, reviving the issues highlighted by Edward Snowden in his NSA leaks.

One figure with knowledge of the work of the intelligence agencies suggested it was highly likely that they knew about "John" and the two British guards of hostages in Syria who were dubbed by their captive John, Paul and Ringo after the Beatles. "I am willing to pay money that the services knew one or all of them," the source said.

Britain's three intelligence agencies – MI5, MI6 and the government's electronic eavesdropping centre, GCHQ – were working together to try to identify the jihadi. MI5 officers were combing their databases to check on movements or associations and former friends which could point to the killer, and to his home address.

Though the hunt is being led by MI5, GCHQ is using all the voice-recognition technology at its disposal, to try to identify the man who recorded a video showing Foley's decapitation.

Counter-terrorism police are understood to be concentrating on local intelligence, hoping to get information from the Muslim and Asian communities. "All security agencies are involved using a variety of means in joint teams", said a source familiar with the operation.

Some 500 Britons are believed to have gone to Syria and Iraq and joined Islamist groups fighting there. Some 200 are estimated to have returned to the UK.

There appears to be a difference of view, however, on the extent of the threat that Isis presents to Britain and other western countries. Former officers from MI6, the UK's foreign intelligence service, have downplayed the threat to British security, while MI5 and the police have emphasised the threat – a view echoed by David Cameron.

The former MI6 intelligence director, Nigel Inkster, urged government ministers to rethink the hardline policy on British jihadis returning from Syria, warning that the current "throw everyone in jail approach" risked advancing Isis's resolve.

He said: "We probably need to start thinking about rather more nuanced approaches to the problem of returning foreign fighters. It is certainly the case that not all these people will be committed, some of them will want a way out. I think there is a need to start developing policies and approaches that might constitute a ramp down which some of these people can be led and brought back into mainstream society. There's no magic bullet here but a one size fits all, throw everyone in jail approach, is perhaps not wise."

Dr Erin Saltman, a counter-terrorism expert at the thinktank Quillam Foundation, said the best chance of identifying "John" would be if he outs himself or if his friends and family in Britain decide to contact the police.

"There is a chance of that because a lot of radicalised individuals have kept their more radical views secret from members of family and friends because they are more moderate and would be shocked," she said. "We can rely on an element of hubris where someone will want to state claim to their actions because of the celebrity that that provides. Those are the best hopes we have," she said.