Bitter splits are emerging between political parties trying to fight a no-deal Brexit, over the new-found unity between Labour and the SNP, with claims they are speaking from the “same script”.

An opposition party source involved in the regular opposition alliance talks said they believed the two parties were meeting up before official meetings to agree a joint stance that Jeremy Corbyn should be interim prime minister and on whether there should be a second Scottish referendum.

Opposition party leaders, including Corbyn, the SNP’s Ian Blackford, the Liberal Democrats’ Jo Swinson, Caroline Lucas from the Green party and Liz Saville Roberts from Plaid Cymru meet regularly in Westminster to consider ways of countering Boris Johnson over no deal and a hard Brexit.

An opposition source who attends the meetings said: “Labour and the SNP are agreeing a script.

“Blackford goes out first to the media and Jeremy Corbyn will come in behind after Blackford has done the hard stuff. He’ll say Corbyn has the right to form a government and we should do this early.

“If feels as if there is this dialogue between the two parties about their own position on interim PM, despite the numbers which have shown Corbyn does not have support across the Commons, and specifically about Indyref2.”

The SNP has blamed the Lib Dems for the hostile briefing, branding it “childish”.

The SNP has in recent weeks agreed publicly with Labour that if there is to be an interim government after a vote of no confidence in Johnson, it is constitutionally correct to allow Corbyn to attempt to lead it as prime minister.

Blackford exclusively told the Guardian last month that the party in Westminster was ready to support Corbyn, should there be a vote of no confidence in Johnson over his Brexit strategy.

He said: “From an administrative point of view, somebody else has to be in office to allow that to happen. Under our constitution, it is the case the official leader of the opposition has the first opportunity to be such a person.”

Swinson has consistently said she does not think Corbyn is fit to be prime minister and would support another person taking on the job of interim leader, such as the former Tory chancellor Ken Clarke or Labour’s Harriet Harman.

An SNP source has previously said it would be too complicated to try and find another figure for people to unite around.

There have been positive noises from the Labour leadership about a second referendum in Scotland. The shadow chancellor, John McDonnell, said in August he would not want to block another vote. More recently Corbyn said it was not a priority for the party should it get into power, and that it was not a good idea, but that he would not rule it out.

It is thought Labour may call on the support of the SNP should it end up being the largest party at an election but short of a majority, and that agreeing to another independence referendum could be the Scottish party’s price. Both Labour and the SNP have so far ruled out a formal coalition.

The race for a Brexit deal: how the day unfolded Read more

One opposition MP said about the cross-party Brexit meetings: “Even in the most casual of conversations, it’s been clear the SNP are trying to use cross-party working to get support for another Indyref.

“With Corbyn making noises about not objecting and the SNP ignoring the numbers to support him as an interim PM, it doesn’t take a genius to see the mutual convenience.”

A Labour party spokesperson said: “Jeremy Corbyn has hosted a series of productive meetings with opposition party leaders in order to work together today to hold the government to account and prevent a disastrous no-deal Brexit.”