At least 50 Labour MPs are prepared to defy Jeremy Corbyn by backing military action to protect civilians in Syria, it has emerged, as cross-party support grows for a new and comprehensive strategy to end the crisis.

In a clear challenge to the Labour leader’s authority, a group of MPs and peers is ready to work with Conservative colleagues to promote a three-pronged strategy in which military intervention by UK forces would complement fresh humanitarian and diplomatic initiatives.

In a sign of increasing cross-party cooperation over Syria, Tory MP and former international development secretary Andrew Mitchell, and Labour MP Jo Cox, a former head of policy at Oxfam, have joined forces in support of the plan in an article for the Observer. Corbyn has consistently made it clear he is opposed to British military involvement in Syria.

British forces could help achieve an ethical solution in Syria | Andrew Mitchell and Jo Cox Read more

Although his close friend and shadow chancellor John McDonnell has suggested Labour MPs could be given a free vote in the Commons, it would be a huge blow to the leader’s authority if a vote was passed with the backing of a sizable number of Labour MPs.

Before the launch by Cox of an all-party group on Syria in parliament on Tuesday, she and Mitchell say that the response of the international community to the Syria crisis, through the UN, has been “woefully inadequate”.

They call for more humanitarian support for refugees from both the UK government and EU, urgent diplomatic efforts to bring President Bashar al-Assad to the negotiating table, and military involvement which has “protection of civilians at the heart of the mission”.

This could include the use of troops to protect new “safe havens” inside Syria, and enforce a “no-fly” or “no bombing zone” to prevent Assad launching further attacks on his own people, as well as moves to hit Islamic State in Syria.

Mitchell and Cox write: “Some may think that a military component has no place in an ethical response to Syria. We completely disagree. It is not ethical to wish away the barrel bombs from the Syrian government when you have the capacity to stop them. The deaths and fear generated by these indiscriminate air attacks are the main drivers of the refugee crisis in Europe. Nor is it ethical to watch when villages are overrun by Isis fighters, who make sex slaves of children and slaughter their fellow Muslims, when we have the capability to hold them back.”

Senior Labour sources say between 50 and 100 of their MPs – including several members of the shadow cabinet – would be ready to back British military action if its ultimate purpose was to protect civilians caught up in a growing humanitarian disaster, rather than merely to extend attacks on Isis into Syria.

David Cameron, who failed in 2013 to win the backing of the Commons for intervention in Syria, has indicated that a fresh vote on military action may be imminent. It is understood he has been told by Tory whips that the number of Conservative MPs who would oppose intervention would be in single figures, and more than outnumbered by the number of Labour MPs who would be prepared to back the move.

On Monday in a Commons debate on Syria, Cox will say that Labour should not allow the experience of Iraq to blind it to the need to back the use of military force for humanitarian ends, as it did in Bosnia, Kosovo and Sierra Leone. She will argue that Cameron has for too long put the issue on the “too difficult” pile following his humiliation in 2013.

John Woodcock, Labour MP for Barrow and Furness, who is joining the all-party parliamentary group, said that MPs must keep an open mind given the human suffering of the Syrian people and the resulting refugee crisis.

“The bottom line is that the killing and the flight of civilians will go on unless the international community can create safe havens in Syria for terrified people who are still being bombed,” he said. “That may well mean greater involvement from air forces to sustain a no-fly zone and will certainly require an end to the hand-wringing over President Putin’s disgraceful deceit in bombing anti-Assad rebels rather than Daesh [Isis].”

Shadow justice secretary Lord Falconer told the Observer: “My position is that the government has to make a military case. There has to be good reason to be doing it, obviously it has to be legal, and we have to consider what the consequences are, including radicalisation here. On the basis that the proper case is made, I think it would be capable of support. But it has to be made and they have not yet done that.”

Corbyn also faces challenges over austerity and immigration. Senior Labour MPs have privately called on him to support the immigration bill, which includes measures to prevent immigrants undercutting British workers. However, shadow home secretary Andy Burnham has insisted that the party will oppose the “kneejerk” bill.

Meanwhile, Scotland’s first minister Nicola Sturgeon is attacking Corbyn’s support for the fiscal charter, which will commit the government to delivering an overall surplus by 2019-20 and to running an overall budget surplus in “normal times”.

She told the Observer: “This week is a key test of Labour’s credentials under Jeremy Corbyn – and it is a test they dare not fail if they are to be taken remotely seriously as an opposition.

“If Labour do not vote against the Tories’ spending proposals, all of their anti-austerity rhetoric will be exposed as empty bluster and will confirm the SNP as the only serious party of opposition in the Commons.

“Jeremy Corbyn has been overruled by his senior colleagues on Trident, and he cannot allow that to happen on austerity too.”