A powerful group inside Jeremy Corbyn’s shadow cabinet is urging Labour to be ready to campaign for a possible second Brexit referendum if Theresa May’s deal is defeated and the party cannot force a general election. The move comes amid signs that support for another public vote is widening at Westminster.

The shadow cabinet alliance pushing Labour to prepare for the option of a second public vote includes Brexit spokesman Keir Starmer, deputy leader Tom Watson, shadow Northern Ireland secretary Tony Lloyd and Richard Corbett, the leader of Labour MEPs in the European parliament.

Support for the idea from top Labour figures comes after shadow chancellor John McDonnell said last week that Labour could well end up backing another referendum, with the option to Remain in the European Union being on the ballot paper.

The Observer can reveal that Starmer told a meeting of the shadow cabinet last Wednesday that Labour should be ready to “move quickly through the gears” to call a no-confidence vote in the government immediately if, as expected, May’s blueprint is defeated when MPs vote on it on 11 December.

As the no-confidence vote is unlikely to pass – meaning the push to trigger an election would fail – it was made clear at the same meeting that Labour should then be ready to take up the option of backing a second referendum campaign if there is no viable alternative.

Starmer received strong support from Watson, Lloyd, and Corbett, with only two shadow cabinet members, Ian Lavery and Richard Burgon, arguing against, according to sources.

It is understood that Corbyn, who had previously resisted the idea of a second public vote, did not oppose the strategy, though he stressed the need to focus on defeating May in the forthcoming “meaningful vote”.

The growing support for the idea of a second referendum at the top of Labour comes after universities minister Sam Gyimah resigned on Friday over May’s Brexit deal and said a second referendum should now be considered.

Gyimah argued that Britain would be “hammered” in future trade talks with the EU if the deal was passed and said that putting the issue back to the people might be the “most sensible” way to resolve the impasse.

“The prime minister has already taken one step in that direction by appealing to the country to put pressure on MPs to vote for her deal,” he told the BBC.

It is also understood that a serving minister has been showing a possible blueprint for a second vote to members of the cabinet, suggesting more MPs could quit to support the idea should May’s deal be defeated.

Shadow cabinet sources said that, while it was entirely right that Labour should focus on defeating May’s deal and trying to force an election, there was wide acceptance that it was unlikely to achieve that goal, so the party would soon be unable to argue that it could negotiate a better deal than May.

One shadow cabinet source said: “So we have to have a policy for when the no-confidence vote fails – a clear line. We should be ready to back a second referendum.”

There is also concern that unless Labour devises a clear line on what its policy will be after Theresa May’s likely defeat, and after it fails to force an election, Corbyn could be exposed in a TV debate that is being planned for two days before the Commons’ meaningful vote.

On Sunday, a cross-party group of MPs, including several Tories, issued a public statement urging party leaders and MPs to rally behind a second referendum as the only way to break the parliamentary impasse.

The group calls on MPs to back a people’s vote amendment to the meaningful vote as a way to build further support across parliament. This, it says, is “the only guaranteed opportunity – written in statute – for the Commons to back a people’s vote.”

Meanwhile, a new YouGov poll published on Sunday shows support for staying in the EU at the highest level recorded by the company since the 2016 referendum. The poll of 1,655 people conducted last week shows remaining in the EU now has a 10-point lead over leaving when people are asked whether or not they want to proceed with Brexit.

In the survey for the People’s Vote campaign, support for staying is now at 55% compared with 45% for leaving the EU once “don’t knows are excluded”. Separate surveys conducted in the four neighbouring London seats represented by Corbyn, shadow foreign secretary Emily Thornberry, shadow home secretary Diane Abbott and Starmer show overwhelming support, and suggest all four would lose votes to other parties if Labour eventually backed a Brexit deal.

While Theresa May, who was attending the G20 summit in Argentina on Saturday, insists she will win over sufficient MPs to get her Brexit deal through parliament, evidence emerged on Saturday night that Conservative activists overwhelmingly oppose the deal. A survey of Tory members by ConservativeHome found 72% of Tory members are against it while only 25% back it.

On Saturday the Japanese prime minister Shinzo Abe urged May to do everything she could to avoid a no-deal Brexit, suggesting that investors from Japan need predictability and stability.

He said he wanted to “pay tribute” to May’s leadership in securing the deal. But he added that any prospect of the UK crashing out of the EU without a deal risked international consequences.

“I would like to once again ask for your support to avoid no deal,” he said. “As well as to ensure transparency, predictability [and] legal stability in the Brexit process.”