Britain edged closer to eventual military involvement in Syria after a senior Labour MP claimed most of his colleagues could defy their leader by supporting the deployment of British forces there, in the wake of the suspected terror attack on a Russian airliner over Egypt.

As thousands of Britons waited to leave Sharm el-Sheikh on Saturday, John Woodcock, a member of Labour’s internal defence committee and MP for Barrow and Furness, said a decisive number of his colleagues could now be convinced about widening Britain’s military involvement into Syria if the government made the case. Jeremy Corbyn opposes any involvement.

The defence secretary Michael Fallon claimed in the wake of the crash that killed all 224 passengers on the Airbus A321 on 31 October that it was “morally indefensible” for Britain to rely on other countries to tackle Islamic State (Isis) when it was a direct threat to the UK’s national security.

The UK is already among a coalition – including the US, France and Australia – fighting Isis militants in Iraq. It is understood that ministers have been privately discussing with both Labour MPs and sceptical Tory MPs what action in Syria might be approved by parliament.

Woodcock said it was time for the prime minister to go public with a strategy in order to win support in the Commons and among the wider public.

The MP, who is a founding member of the all-party Friends of Syria group of MPs, said: “I think Jeremy Corbyn’s and [shadow international development secretary] Diane Abbott’s views on this are probably set in stone and probably have been for the last 30 years.

“But I think the majority of Labour MPs will feel, yes, the party whip is important, but that they have an individual responsibility as an MP, aside from party allegiance, to make what is the right, although always difficult, decision to consider putting UK forces potentially in harm’s way. I think the majority are open-minded, but they want to see a plan.”

The number of Conservative MPs who would oppose intervention in a vote is likely to be in single figures, but Downing Street is yet to be convinced that there are enough opposition MPs to secure victory in a vote.

The Labour MP’s comments suggest that the Tory rebels could now be more than outnumbered by the number of Corbyn’s MPs prepared to back the move, despite their leader’s opposition to it.

Crispin Blunt, the Tory MP who chairs the foreign affairs select committee, dismissed Fallon’s comments but also said it was time for a strategy to be laid out for parliament to consider.

He told the Observer the suspected terror attack on the Metrojet airliner over the Sinai peninsula would usher in greater cooperation with Russia, but that the government had yet to provide a convincing rationale for British forces adding their weight to coalition attacks on Isis strongholds outside of Iraq.

“We need a convincing comprehensive strategy. The moral imperative, as Michael Fallon describes it, to mobilise the entirety of eight RAF jets, doesn’t do the trick,” said Blunt. “We need to be clear: is this going to work and is it legal? If we can answer those questions satisfactorily, then go for it.”

About 1,400 people were returned to the UK on Friday from Sharm el-Sheikh and another 1,500 were expected to leave on Saturday, but it is expected to take a further 10 days to repatriate all of the British tourists stranded at the Red Sea resort.

A British government spokesman said: “With a limited number of flights able to leave Sharm el-Sheikh each day for the UK, it is likely that tour operators or airlines will advise some people to extend their stay at their resort.”

Egypt’s civil aviation minister, Hossam Kamal, said the volume of luggage being left behind by British passengers had disrupted operations at the airport, and that a large number of scheduled flights had been cancelled.

Of 29 services scheduled on Friday, 21 were cancelled by the Egyptian authorities and some planes were forced to divert in mid-flight.

There are also an estimated 70,000 Russians at the resort and in Hurghada, on the other side of the Red Sea.

The Russian deputy prime minister, Arkady Dvorkovich, said his country’s nationals would not be flocking to come home. “Tourists will be returning from Egypt to Russia when they planned to,” he said.

The head of an investigation committee into the crash, Ayman al-Muqaddam, confirmed on Saturday reports that there was a noise at the end of a cockpit recording from the crashed Russian jet.

Al-Muqaddam said experts were still gathering information and it was too soon to announce their conclusions. The British transport secretary, Patrick McLoughlin, said information obtained by UK officials indicated that there was a “high probability” that the aircraft was brought down by an explosive device.