Downing Street has disputed claims by the Scottish Government that Sir Keir Starmer has agreed to talks that will include a second independence referendum.

The meeting is scheduled for next month – assuming Sir Keir is still Prime Minister – and was agreed in a call from Downing Street congratulating Mr Swinney on his election success.

However, No 10 has disputed the SNP leader’s claims that a referendum will be discussed and has insisted that the UK Government remains opposed to another independence vote.

The offer came amid ongoing turmoil in the UK Government as almost 100 Labour MPs demanded the Prime Minister quits. He will meet Health Secretary and leadership contender Wes Streeting ahead of Wednesday’s King’s Speech.

After a short Cabinet meeting Sir Keir insisted he would carry on despite suggestions that rivals, including Energy Security Secretary Ed Miliband, were lining up a challenge. Four junior ministers have resigned: Miatta Fahnbulleh, Jess Phillips, Alex Davies-Jones, and Zubir Ahmed.

The talks with John Swinney, who will be installed as Scotland’s First Minister next Tuesday, came without warning.

A spokesperson for the First Minister earlier said: “The First Minister is pleased that the Prime Minister reached out to congratulate him on his emphatic election win and that the Prime Minister stressed his willingness to work in collaboration with the Scottish Government where possible.

“It is particularly welcome that the Prime Minister agreed to meet next month to discuss a referendum on independence.

“Given the SNP’s landslide victory and the fact that the people of Scotland have elected more pro-independence MSPs than at any point in the Parliament’s history, the previous refusal of the UK Government to consider Scotland’s right to decide its own future was clearly unsustainable.

“A way forward must be found and so these discussions are welcome.

“Coming alongside Labour MSPs making clear that there must be a way for this question to be resolved, it is now very clear that the momentum is building behind Scotland’s right to decide.

“The First Minister looks forward to the talks with the UK Government, and is confident that the people of Scotland will choose the fresh start of independence.”

A Downing Street spokesperson poured cold water on the suggestion that Sir Keir would entertain another referendum, saying: “The PM committed to meeting to discuss shared issues including the cost of living.

“As the PM told the First Minister, the manifesto this government was elected on was unambiguous that Labour does not support independence or another referendum.

“Our position remains unchanged.”

On speculation that the talks would include the referendum, Scottish Conservative leader Russell Findlay said: “We warned during the election campaign that if Swinney achieved his self-imposed ‘mandate’ of an SNP majority, Starmer would be likely to surrender to his referendum demands. 

“If he wasn’t so weak, Starmer would have sent Swinney packing and told him to get on with the day job.”

Bond markets remained jittery amid the speculation over the future of Sir Keir Starmer. The yield on the 30-year gilt, which reflects the market’s views about long-term debt sustainability and economic growth, rose by 0.13 percentage points to 5.81%, the highest since May 1998.

Mohit Kumar, chief European economist at Jefferies, said investors should bet against the pound as a change in the composition of the government “would likely be left-leaning”.