Wes Streeting has held talks with Keir Starmer in Downing Street as an ally of the health secretary renewed calls for the prime minister to resign, saying his authority had “irretrievably ebbed away”.

Streeting arrived in No 10 on Wednesday morning amid intense speculation over Labour’s leadership crisis and his own future within the party. He left approximately 16 minutes later without commenting to the media.

The health secretary’s allies had sought to portray Wednesday’s meeting as a moment for Streeting to speak candidly about his concerns. But No 10 insiders suggested Streeting was playing down speculation that he was on the brink of declaring his candidacy for the leadership.

The meeting came shortly after Dr Zubir Ahmed, who resigned from his junior health minister role on Tuesday, blamed Starmer for Labour’s disastrous local election results and urged the prime minister to set out a timetable for his departure in “an orderly expedient transition”.

Ahmed accused Starmer of becoming the “inadvertent midwife of a fifth-term SNP government” in Scotland’s parliamentary elections, saying Labour had been unable to challenge the Scottish National party because of “noise created at the centre”.

The NHS transplant surgeon told BBC Radio 4’s Today programme: “We, in Scotland, as in the rest of the UK, had a devastating set of election results and we were simply unable to articulate our offering, or indeed critique, of the SNP government because of the noise created at the centre.

“Therefore, we became, and the prime minister became, the inadvertent midwife of a fifth-term SNP government. And that scenario you saw then, people waiting for a speech to try and articulate his new direction, a strategy, and it simply was not forthcoming. And you saw thereafter a spontaneous outpouring of frustration by colleagues in the PLP [parliamentary Labour party].”

When asked if the reaction among Labour MPs had been spontaneous, Ahmed said: “This is not one faction of the Labour party. This is about the Labour party articulating, I think, now a commonly held view that this is unsustainable and unstable.”

Ahmed’s intervention risked widening scrutiny around Streeting’s positioning after days of speculation over whether he could emerge as a potential leadership contender for MPs seeking a post-Starmer future.

While Streeting has remained publicly loyal to Starmer since the local elections, several of his allies have resigned from the government in recent days, including four junior ministers, openly calling for Starmer to go.

Starmer’s allies sought to portray the prime minister as having survived the most immediate threat to his leadership, after a Streeting-led challenge failed to materialise before the king’s speech on Wednesday.

Nick Thomas-Symonds, the Cabinet Office minister and longstanding ally of Starmer described the meeting as a simple “coffee”, mocking the speculation around the meeting.

“Anyone would think we were talking about the final scene at Casino Royal,” he told the BBC. Thomas-Symonds said there was no viable leadership challenge against Starmer, claiming Labour rebels had failed to unite around an alternative candidate capable of securing the backing of 81 MPs as required under party rules.

“The evidence of the last two days is that there isn’t an alternative candidate with 81 MPs,” he said.

With Downing Street insiders desperately seeking to project calm before the arrival of King Charles in the House of Lords for the king’s speech, pressure on Starmer continued to build elsewhere.

The Guardian revealed on Tuesday night that 11 Labour-affiliated unions were predicting Starmer would not lead the party into the next general election. The unions, which include Unite, Unison and the usually loyal GMB, were expected to issue a joint statement on Wednesday saying that “at some stage” the party would have to put a plan in place to elect a new leader.

In a leaked copy of the statement, the unions said it was clear to them that Labour “cannot continue on its current path” and that despite some progress it was not doing enough to deliver the change people voted for at the general election.

The union general secretaries wrote: “Labour’s affiliated unions have been clear that Labour cannot continue on its current path … the results at the election last week were devastating … Labour is not doing enough to deliver the change that working people voted for at the general election.”