Britain’s main political parties are moving towards an agreement to recall parliament on Friday to allow MPs to approve British involvement in air strikes against Islamic State (Isis) forces.

David Cameron – who will attend a meeting of the UN security council in New York chaired by Barack Obama on Wednesday in the wake of US air strikes against Isis forces in Syria – believes it would be politically impossible for him to proceed without the support of Labour.

The opposition Labour leader, Ed Miliband, whose intervention during an emergency recall of parliament last year helped to stop air strikes against the regime of Bashar al-Assad in Syria, is expected to have talks with the prime minister later this week.

There is a growing consensus that there would be a legal basis to launch strikes against Isis forces in Iraq, not least if the government in Baghdad requests British involvement. There is less agreement in following the US example in launching strikes against Isis in Syria.

Chuka Umunna, Labour’s business spokesman, said the situation with Isis was different to the situation in Syria last year when the party opposed strikes against the Assad regime after a chemical weapons strike in a Damascus suburb. He said the party would apply the same principles that it applied a year ago. Labour sources stressed that these principles were used when the party supported military action in Libya.

Umunna told BBC Radio 4’s Today programme: “A request for support hasn’t been put in yet, as far as I understand. If it was we would apply the same criteria to judge what position we adopt in relation to any proposed action as that we applied last year in respect of the proposed intervention in Syria.

“The three principle criteria are: what is the basis in international law for intervention? Second, what is the plan of action in respect of any action? And, thirdly, what is the plan for what happens after, of course learning the lessons of Iraq.”

But Umunna spoke of how the circumstances were different this time. “I do think the public draw a distinction between the [Isis] situation and what was being proposed in Syria last year. I think the public is in a different place on the Isis issue.”

He added: “[Isis] need to be eliminated. They are an evil organisation. What we have seen them doing – beheading people, persecuting the Yazidis – is absolutely inexcusable and we have not seen a group engage on this scale in such an organised manner for some time.”

Jack Straw, the former Labour foreign secretary, indicated that Miliband would respond seriously to a request for support from Downing Street.

Straw told the Today programme: “I know it would be given a very sympathetic hearing as it will be by the parliamentary Labour party. Last year’s debate was about strikes against the Assad regime. This year’s debate is a very different one – it is about strikes against the enemies of the Assad regime. That is an illustration of how quickly circumstances have changed in the region. Yes, the Assad regime is a bad regime and brutal. But on any metrics the medieval barbarians of ISIL [Isis] are in a league of their own and they have to be dealt with.”

Straw held out the possibility of joining strikes against Isis in Syria. He said: “It depends on the circumstances – Syria only if there is consent of some kind by the Syrian government because there are quite big legal problems if there is no consent. What is encouraging about what has been announced overnight is that there is an alliance of Arab countries involved in this because it should not just be seen as the Satans of the west coming in to defend their interests.”

On Monday, Jim Murphy, Labour’s international development spokesman, said air strikes in Syria to destroy Isis would not be “illegal” as Washington does not recognise the legitimacy of President Assad.

Quizzed at a fringe meeting on Syria, organised by humanitarian aid charities WorldVision and Islamic Relief, Murphy told delegates that “air strikes are part of the answer”.

When he was pressed over whether dropping bombs in Syria would be legal given the regime in Damascus has refused permission for foreign jets to strafe Isis positions, Murphy replied: “America has said that they are not seeking Assad’s [permission]. They don’t recognise Assad. It’s important that America is trying to stop the humanitarian slaughter with air strikes. The Labour party is not opposed to trying to save people’s lives.”

Senior figures in the party were surprised that such a senior Labour figure would take such a position on what is a tricky issue for the party, ahead of a crucial Commons vote on whether the UK should be backing the US in bombing Isis strongholds in Syria.

Tom Watson, the former Labour party chair, tweeted to say: “surely (Murphy) wouldn’t be that ignorant of international law?”

Murphy was demoted last year from his position as Labour’s defence spokesman to the post of shadow international development secretary after he expressed unease over Miliband’s stance on Syria.

Last year, the government was defeated on taking military action in Syria after Labour refused to support Cameron’s stance. After the vote, Murphy claimed that Labour MPs, including himself, had not wanted to rule out military action in Syria and the party had not expected the vote’s outcome. “It’s not what I wanted,” he wrote on his blog. After that outburst he was demoted to the international development brief.

On Tuesday, however, Murphy appeared unrepentant in that view, reminding party activists that in spite of the ghosts of Iraq, Labour does still support intervention. “Community does not stop at the end of your doorstep. After one and half unpopular wars in Afghanistan and Iraq, what can be the progressive instinct to Syria’s civil wars? What I don’t want is to create a permanently unpopular concept (of inaction).”

Murphy has not been a central figure over the past year though he has revived his career after playing a key role during the Scottish referendum campaign.