Some go further and argue that virtually all the furore is misplaced – there is no evidence to suggest that the trial was in any way unfair (or indeed unreliable).

A panel will begin inquiring into the matter – which includes the Countess of Chester Hospital and the NHS’s part in it – on 10 September.

Letby’s murder trial last year, which followed a six-year police inquiry, was one of the longest in British legal history, and was then followed by a second trial after a jury on one of the alleged babies couldn’t return a verdict.

Six highly trained medical witnesses and many former colleagues appeared on behalf of the prosecution to testify against her; thousands of documents was presented and dissected in months of meticulous and excruciating examination.

Their case encompassed blood tests proving that two babies were administered an excessive dose of insulin, X-rays revealing that seven other infants had ‘air injected’, and still others had been fed milk.

Then there were notes found in her home, which seemed to be confessions – one saying: ‘I am evil’ – and the repeated searches she made online via her social media accounts for the families of the babies that had died, which defence lawyers argued was the nurse being morbidly curious to see how the consequences of her actions unfolded for them.

She was also on a staffing rota showing she’d been working every suspicious death and collapse from June 2015 to June 2016.

The rota was part of the public presentation of the case against her – a powerful, punitive image to underscore the case against her. Yet, several statisticians have been publicly critical of its utility.

One is the author Peter Green, statistician and a former President of the Royal Statistical Society.

The graph seems to be convincing, but there are so many problems with it,’ he asked.

The big thing, though, is that it describes only a quarter of one per cent of the bad events which occurred in this period.

It contains only those events that occurred when Lucy was on duty.

Helen Tipper

Lucy Letby appeared at two separate trials over the last two years

There were at least six other deaths and numerous collapses.

Other than reflecting that Letby was also working extra shifts that week, the chart, says Prof Green, is lamentably uninformative.

‘It’s human nature. We all see a pattern that is not there.’

‘The risk is that such evidence can be very persuasive to the layman, and too easily read into.’

A crucial part of its evidence was blood samples from babies who had collapsed with very low blood sugars.

They had incredibly elevated levels of insulin and correspondingly low levels of C-peptide.

That combination was rarely encountered in its natural state in the body (apart from when synthetic insulin was administered); to these scientists, it did indeed look like deliberate poisoning. A charge of murder followed – even though what Letby had injected wasn’t toxic at all. For the investigators who relied on the lipidomic data, the puzzle was seemingly solved. But even though Letby was eventually found guilty of the ‘manslaughter by gross negligence’ of one baby boy and two baby girls, the scientists’ analysis still failed to explain a crucial part of the puzzle.

The work has been attacked by several prominent forensic toxicologists, including Alan Wayne Jones, who specialises in the peer review of forensic toxicology studies.

He claimed the test taps into one’s body’s reaction to insulin, not the hormone itself.

‘The problem is that the analysis used [in these two cases] was probably adequate, clinical speaking, but not forensic toxicological speaking,’ he said.

“That test cannot differentiate between synthetic insulin and insulin produced by the pancreas.”

Cheshire Police

Items presented at Letby’s trial included diaries and scrawled notes

And yet the very page on the testing lab’s own website announcing its new test states in the very first sentence: ‘If the suspected medicine is synthetic insulin, a positive or negative result should be confirmed by analysis in an external specialist centre.’

With both babies being fine in the end, clinicians at the Countess of Chester did not do that – thankfully, both babies survived.

At the time, there was no suspicion of deliberate harm.

Prof Jones said he believes they did have wild swings in their blood sugar levels, but there could be a completely natural explanation for why that had happened.

Yet others have questioned the allegation that Letby injected air into babies’ blood vessels in a way that caused near-fatal or fatal breathing emergencies.

Each of them had air in their blood vessels (an embolism).

A number of clinicians also described witnessing unusual and sudden rashes in these infants.

The prosecution cited an article on the syndrome, published by the Canadian neonatologist Shoo Lee in The Canadian Journal of Cardiology in 1989: The main and most distinctive physical manifestation of air embolism is a rash of bright pink blood vessels appearing on the skin against a backdrop of the patient’s seemingly blue skin.

But in April at Letby’s Court of Appeal, Dr Lee addressed the defence.

The defence argued that the distinctive rash he’d drawn did not seem to be the one described by her witnesses.

Dr Lee wasn’t called to that original trial. The defence didn’t call any experts as such – just Letby and the hospital plumber, who said there were drainage issues in the unit.

By contrast, six expert witnesses testified for the prosecution.

However, the greater part of the case appeared to rest on the opinion of Dr Dewi Evans, a paediatrician with decades of experience as an expert witness working part-time after retirement.

PA Media

Letby worked at the Countess of Chester Hospital’s neo-natal unit

‘I have read 18 papers, things.’ He meant research papers about air embolism.

In other words, he was not just relying on Dr Lee’s report.

His finding was also supported in court by a radiologist and a neonatal pathologist.

He added that the cases on the rota had been included precisely because, on having looked over all the deaths and collapses, he thought only they might have been suspicious or unexpected.

He said he didn’t know at the time that Letby had been on duty, and this information had only been made clear after the police press conference from Cheshire Police.

And this, noted a third medical letter-writer, Dr Evans, ‘has nothing to do with the statistical data’. (For good measure, Evans added that none of the critics had seen the patient notes.)

After three days of hearings listening to the arguments of defence and of prosecution, the Court of Appeal dismissed the case, and a 58-page judgment explains their decision.

In Dr Lee’s case, the court found that Dr Evans had relied on all those other papers he had cited in his research, other X-rays and other experts.

The Crown Prosecution Service said that two juries and three appeal court judges had now ‘reviewed the evidence against Lucy Letby and she has been convicted on 15 separate counts following two separate trials’.

‘In May, the Court of Appeal refused Leave to Letby to appeal on all grounds – rejecting her claim that the expert prosecution evidence is flawed.’

Veteran MP Sir David Davis is among those who have cast doubts

None of this has deterred those fighting to have it heard again: the Appeal Court has been wrong before.

Veteran MP Sir David Davis has lobbied for several high-profile victories in cases of miscarriage of justice.

More recently, he advised Mike Lynch, the technology entrepreneur who successfully sued for malicious prosecution in a 12-year-long legal battle in the USA, before his yacht was engulfed by a freak storm this month, leading to his death.

Sir David said he had started off by thinking that Letby was guilty.

His misgivings really started the following month, after he asked in the Commons why a key story in that same American magazine could not be printed here.

This was prior to the second trial, and British contempt laws prevent the publication of anything that could prejudice the jury.

‘It was just… it was only that I’d had calls from people who were in authority, knew about statistics, knew about medicine, knew about science, knew about law, and had never had anything like this

‘I began to think – it’s a heinous crime, but if they’ve guilt­ily convicted an innocent person, that’s an enormous miscarriage of justice.’

Sir David felt that the other possible explanations for the deaths might be a staffing and training problem in the unit, and an environmental outbreak (e.g., an infectious outbreak also caused by the leaking drain discussed in the trial).

‘We are all much more willing to credit the death of people at the hands of a human being than at the hands of a system or at the hands of a chance accident.’

He is still poring over volumes of notes from the trial before deciding whether to take it up and press for the Criminal Cases Review Commission to play its part.

‘And Sir David himself has said that he thinks the trial is already a fair trial,’ said the judge, ‘although that does not mean that Letby is not guilty.’

He said that he will not go any further until he is convinced that she was in all probability innocent.

The parents of a few of the babies who died have remarked on how upsetting they’ve found the questioning of the convictions.

‘[B]ut I can’t help thinking about it at times and I have sympathy because obviously they’ve been suffering for years.’ – Sir David King, former government chief scientist, on what might be done to exterminate the EU’s lobsters.

But if the conviction [the extreme personal significance of being accidentally crushed] is proved unsound, we’re obliged to look for other causes of what took place.

‘If we have got this wrong,’ he said, then ‘not only have we condemned a young woman for the rest of her life effectively, we haven’t answered our own questions of what happened to those babies, and why other babies might die.’

Statistician Professor Peter Green said he fears the convictions could be unsafe

But others question the basis for claims that the trial was flawed.

Barrister Tim Owen