Britain’s most senior civil servant has condemned “malicious” Whitehall smears about Jeremy Corbyn’s health and promised an independent input into his investigation into the affair, Labour has revealed.

In a private meeting with Corbyn in parliament, Sir Mark Sedwill – who is also Theresa May’s national security adviser – acknowledged the seriousness of the attack and pledged to complete his probe as soon as possible.

HuffPost UK has learned that a civil service commissioner, an outside expert independent of government and officials, will take part in the investigation.

The row erupted after the Times reported claims last weekend that two senior mandarins had gossiped that the Labour leader was too “frail” and lacked the mental capacity to become prime minister.

One civil servant was quoted as saying “there must be senior people in the party who know that he is not functioning on all cylinders”.

Another said “there is a real worry that the Labour leader isn’t up to the job physically or mentally but is being propped up by those around him”.

Corbyn and shadow minister Jon Trickett used a “frank” 45-minute meeting with Sedwill on Wednesday evening to warn that the credibility of the investigation would be judged on whether it unearthed and disciplined the culprits.

Sedwill agreed that there should be an “independent” element to his inquiry, after the Labour leader warned that the political neutrality of the civil service was at stake.

One of the UK’s civil service commissioners, outsiders with a statutory oversight of Whitehall, will play a key role, insiders said.

The investigation is being conducted by the Cabinet Office, but Corbyn’s spokesman had warned that the civil service could not be seen to be “marking their own homework” on such an important matter.

A Labour Party spokesperson said: “The meeting was frank and detailed, with a full exchange of views.

“The seriousness of the civil service breach and the evident malicious intent behind it was acknowledged by all participants in the meeting.

“Jeremy Corbyn and Jon Trickett pressed the case for a fully independent investigation to restore trust and confidence in the civil service.

“They were promised an independent element to the civil service investigation, that they will receive regular updates on its progress and that it would report as soon as possible.

“They made clear the credibility of the investigation will be assessed on the basis of its results.”

Before the meeting, Corbyn’s spokesman told reporters that the claims made by the unnamed officials at the “apex of the civil service” were “completely out of order” and “unprecedented”.

“[They were] briefing on the basis of false information – namely that he is ill, or his health is significantly impaired. That is entirely untrue so on both counts you’re talking about a very serious breach of civil service neutrality – the principle that absolutely underlines our democratic constitution.

“There needs to be action taken and there needs to be measures taken to restore confidence and trust,” he said.

“Quite clearly in the light of what has taken place that has been undermined, that trust has been broken and it must be restored, not just for us or for Jeremy Corbyn but for the healthy functioning of our democracy. That’s been recognised for getting on 200 years.”

The spokesman said that Corbyn was fit and healthy and his only medical issue was a squint in one eye caused by a muscle problem that was being treated.

He said: “We have been open about his medical issues. We have put in the public domain that Jermey has a muscle weakness behind one eye which people will have noticed that has led to some squinting in public and that’s an easily fixable problem, it’s not a serious problem and that is the limit of his health problems.”

Downing Street insisted a civil service investigation is the correct way to proceed.

“The civil service is responsible for looking into any potential breaches of the civil service code and this is no different,” the Prime Minister’s official spokesman said.

“If we are able to identify any individual responsible we will take appropriate disciplinary action.”