Almost half of Theresa May’s cabinet have held talks to weigh up the possibility of backing a soft Brexit option as a plan B if parliament rejects the prime minister’s EU withdrawal deal.

Four cabinet ministers have held meetings to discuss the “Norway plus” plan amid concerns at the top of government that May will struggle to muster enough votes to get her proposals through the Commons.

Five other, remain-backing ministers – David Lidington, Philip Hammond, Amber Rudd, David Gauke and Greg Clark – are understood to have agreed to try to get the prime minister to support a softer departure from the EU.

Their favoured option is believed to be staying in a permanent customs union, which is currently Labour policy, increasing the likelihood of the plan making it through the Commons. “We see that as the best way of guaranteeing frictionless trade if the deal falls,” one said.

The group have been meeting weekly for some time, either at the Treasury or in their Commons offices, to discuss the government’s options if the deal is defeated. “They just don’t make as much of a fuss about it as their Brexit-supporting colleagues,” one source said.

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Nick Boles, a former minister and a leading advocate of a Norway-style departure from the EU, confirmed that he had spoken to four cabinet ministers, thought to include Michael Gove, a leading Brexiter, about his proposals.

Supporters of the Norway plus campaign, which is pushing for the UK to join the European Free Trade Association (Efta) and have a customs arrangement with the EU, believe Tory MPs and ministers should start to apply pressure on May to swing behind it.

The campaign for Norway plus has gathered momentum since the SNP leader, Nicola Sturgeon, and the DUP’s Arlene Foster – who have both said their parties would not support May’s deal – indicated in recent days they would consider the option.

“Everyone is looking for a plan B. There is gathering momentum for Norway plus. We are seeing the makings of a parliamentary majority,” Boles told the Guardian.

“We have to take on the chin that the EU have said they won’t negotiate the withdrawal agreement. But they might be prepared to renegotiate the political declaration.”

Boles has also held talks with Labour MPs, 75 of whom defied party instructions to abstain from voting for European Economic Area (EEA) membership in June.

He hopes the majority could be persuaded to back his plan, although a number have now come out for a second referendum.

He said: “Labour MPs want to be able to fulfil their obligations to their leadership and party members before being asked to support Norway plus. That’s why it needs to be a fallback plan that comes into play after all the votes have happened and all other avenues have been closed off.”

However, even supporters of the Norway plus plan acknowledge it would present difficulties for the prime minister, whose key Brexit red line is to end freedom of movement. Efta members are obliged to admit workers from elsewhere in the EEA.

Supporters argue, however, that the “emergency brake” that exists for members would allow the UK to cap migration in extreme circumstances, while the government has begun registering all EEA nationals already in the UK, meaning that if they fail to find work within a few months, it will be able to remove them.

May’s official spokesman said: “The prime minister believes the deal that she has delivered is the right one for the country and one of the main reasons for that is that it allows us to take back control on our borders by ending freedom of movement.”