Labour's shadow chancellor has said its MPs should be allowed a free vote on taking military action against Islamic State in Syria, after reports that some of his colleagues might quit if forced to vote against bombing.

With Labour deeply split over Syria two months into far-left lawmaker Jeremy Corbyn's leadership, John McDonnell said MPs should be allowed to follow their conscience on issues such as going to war

"You're sending people out possibly to die," McDonnell – a close ally of Corbyn – said on BBC radio late on Friday.

"There shouldn't be any party discipline on issues like this. You should follow your own judgment of what's best in the interests of the constituency and the country."

Prime Minister David Cameron wants to convince parliament to support British air strikes against Islamic State in Syria as well as in Iraq where it already supports US-led attacks.

drive to win support in parliament has taken on fresh urgency after the attacks by gunmen in Paris this month which killed 130 people and were claimed by Islamic State.

French President Francois Hollande said on Friday he hoped Britain's lawmakers would back Cameron on the issue.

Corbyn has written to his party saying he could not support the case for military action. But some members of his top team have said they believe that extending the bombing is right.

Former Labour Prime Minister Tony Blair's decision to join the US-led Iraq war in 2003, in which 179 British service personnel were killed, remains contentious in Britain after questions were raised over the intelligence case for action.

An opinion poll suggested 48 per cent of British voters supported extending air strikes to hit Islamic State in Syria with 30 per cent opposed. The poll, carried out by polling firm Survation for the Daily Mirror newspaper, also showed 49 per cent favoured diplomatic and non-military options before committing Britain to anything more than air strikes.

The split within Labour has led to speculation that Corbyn will face a mutiny. The Times newspaper said senior Labour officials and lawmakers had sought legal advice on how to unseat Corbyn in the hope of building support for a plot against him.

A Labour Party spokesman said he was not able to comment immediately on the report.

Most Labour lawmakers did not support Corbyn's bid for the leadership but he was backed by an overwhelming majority of grassroots party members.

Anti-war demonstrators were due to march in London later on Saturday against the extension of military action by Britain.

Cameron lost a vote in parliament on air strikes against Syrian President Bashar al-Assad's forces in 2013. He has said he will only call a vote on launching bombing raids against Islamic State in Syria if he is sure of winning enough support.

The BBC said on Saturday government ministers had written to Labour lawmakers to make the case for taking military action.