John McDonnell has denied plotting to oust Jeremy Corbyn as Downing Street left the door open to holding a leak inquiry after senior civil servants said they were concerned the Labour leader was too 'frail' to be PM.
The shadow chancellor has been accused in recent days of hatching a plan to get rid of Mr Corbyn and install a more pro-EU candidate as his replacement.
But today he dismissed the idea of a 'split' between the long-time allies as he insisted he was united behind Mr Corbyn.
It came as Number 10 said that Cabinet Secretary Sir Mark Sedwill will write to the Labour leader in the coming days about the explosive civil service comments about Mr Corbyn's health.
The Prime Minister's official spokesman suggested the briefings to The Times which were published on Saturday risked damaging the impartiality of the civil service and described the comments as 'inappropriate and unacceptable'.
The publication of the comments, which also included suggestions that Mr Corbyn was 'losing his memory', sparked a political firestorm.
Mr Corbyn, 70, hit back and demanded an inquiry to establish who had been 'spreading fictitious information' to the press.
Meanwhile, his allies defended his suitability to be prime minister as Len McCluskey said his friend was 'fit as a fiddle'.
Downing Street did not rule out holding an inquiry into the remarks.
The PM's spokesman said: 'Impartiality is one of the fundamental values of the civil service and underpins its ability to effectively serve the government of the day.
'It would clearly be inappropriate and unacceptable for comments of this sort to have been made or briefed to the press.
'The Cabinet Secretary will be writing to the leader of the opposition shortly.'
Asked directly if there would be an inquiry, as demanded by Mr Corbyn, the PM's spokesman said: 'I think it is right that the Cabinet Secretary responds to the Leader of the Opposition first.'
Mr Corbyn was spotted out riding his bike yesterday as reports about his health continued to cause waves
John McDonnell has been accused of plotting to oust Mr Corbyn amid reports the pair have clashed over Labour's Brexit policy
Mr Corbyn is believed to favour the shadow business secretary Rebecca Long-Bailey as his future successor
Mr McCluskey told the BBC yesterday: 'Jeremy Corbyn is fit as a fiddle, he is one of the strongest people I have ever met - people 20 years younger struggle to keep up with him...'
Tensions have escalated between Mr Corbyn and Mr McDonnell recently over the party's approach to Brexit.
Mr McDonnell has been trying to persuade Mr Corbyn to back a second referendum and to commit Labour to campaigning for Remain.
But he said today the two men had not fallen out.
'We've agreed any deal or no deal has to go back to the people in a public vote & now Jeremy is consulting on our position in that vote,' he said.
'I have expressed my view as have others. That's democracy.'
Mr Corbyn mounted a furious counter-attack after it was reported that senior civil servants thought he might be forced to stand down because he is not up to the job 'physically or mentally'.
Labour has demanded that the 'totally unwarranted and unconstitutional political intervention' by civil servants be investigated.
Shadow cabinet office minister Jon Tricket has written to Cabinet Seceretary Sir Mark Sedwill insisting on an independent probe into leaks about Mr Corbyn's health, saying they were an 'apparent breach of civil service neutrality.
In his letter Mr Trickett wrote that the reports in yesterday's Times 'offer a credible account of conversations at a senior level in the civil service about the Leader of the Opposition'
'The premise of these conversations is the allegation that Mr Corbyn's health is poor. This is manifestly untrue.
'Discussion of these matters, based on false assumptions, should not be taking place.
'Worse, it is without precedent in my experience that any high-level discussion about senior politicians, let alone the Leader of the Opposition, should be shared with a newspaper.
In an angry statement, Mr Corbyn said that it 'should be very concerning to all of us' that civil servants 'should be briefing a newspaper against an elected politician, against a prospective government'.
He added: 'The Civil Service has to be independent; has to be non-political and has to be non-judgmental of the politicians they have a duty to serve... That is the way British democracy must work.
'There must be an investigation into which senior civil servants are spreading fictitious information to the press and in the process compromising the integrity of the Civil Service.'
Mr Corbyn's team moved swiftly to counter the civil