It was June 2016, and almost a year had passed since Stephen Brearey, the lead doctor at a neonatal unit in northwest England, first became concerned about a spate of troubling and unexpected deaths on his ward.

Five babies had died, and at least six others had experienced unusual complications. The neonatal ward at the Countess of Chester Hospital cared for premature and vulnerable babies, but the number of deaths was far above average for the unit. Something was desperately wrong.

Then, in the early evening of June 23, a baby boy — one of a set of newborn triplets — suddenly became sick and died. The following night, as the parents were still reeling, another of the triplets died.

The infants had been in the care of Lucy Letby, a seemingly conscientious and well-liked nurse. Dr. Brearey had noticed that she was present in every other suspicious case and raised that fact multiple times with executives, but he felt his concerns were dismissed.

After the second triplet died, he phoned a hospital executive and demanded that Ms. Letby be removed from the ward. The executive said there was no clear evidence against the nurse and insisted she was safe to work with, Dr. Brearey later told a court.

It would be another week before Ms. Letby, now considered the most prolific killer of children in modern British history, was moved to clerical duties, and months before the hospital’s senior managers contacted the police.

She was finally convicted last week of killing those boys by injecting air into their bodies, murdering five other babies and attempting to murder six others in her care.

The harrowing case has not only horrified the nation but raised profound questions about the workplace culture that allowed her to continue working, even after doctors raised alarms.

Since the trial, clinicians who worked alongside Ms. Letby have spoken out, describing a culture of hostility toward whistle-blowers and a fear of scandal that they say meant their alerts were ignored.

The hospital delayed contacting the police.

In England, hospitals that are part of the National Health Service, or NHS, are operated by individual trusts that have their own management teams. The Countess of Chester Hospital Foundation Trust did not contact the Cheshire Constabulary, the police force responsible for the area, until early May 2017, a year and a half after doctors first began reporting their suspicions.

During the trial, the court heard that a number of pediatricians who worked alongside Ms. Letby, 33, including Dr. Brearey, had repeatedly alerted hospital executives to their concerns about the nurse.

Dr. John Gibbs, who worked in the department, told Channel 4 news that there had been “resistance on the senior management side to involving the police, but I don’t know quite why.” He added, “We pediatricians were certainly concerned that someone — and suspicions fell on Lucy Letby — could have been harming and perhaps killing patients on the unit.”

After Ms. Letby left the unit, she began a grievance case against the hospital, claiming she was being victimized. In January 2017, some of the doctors were made to apologize to the nurse and asked to attend mediation sessions, including Dr. Brearey and Dr. Ravi Jayaram, a pediatrician at the hospital for nearly two decades.

Dr. Jayaram had spoken up about Ms. Letby as early as October 2015 and recently told ITV he believed “babies could have been saved” if the situation had been reported to the police earlier.

“There are things that need to come out about why it took several months from concerns being raised to the top brass before any action was taken to protect babies,” Dr. Jayaram said in a statement on Facebook on Friday, “and why from that time it then took almost a year for those highly paid senior managers to allow the police to be involved.” He declined an interview request from The New York Times.

The case highlights a problematic culture in the health service, experts say.

Medical professionals say the fact that the trust failed to involve the police sooner underlines a broader failing in the NHS. Rob Behrens, an ombudsman who investigates complaints about government departments and the health service in England, said the trial revealed how, for too long, nobody listened despite repeated alarms.

Mr. Behrens was clear that the type of intentional killing seen in Ms. Letby’s case was extremely rare in the health service. But he said that senior managers’ ignoring warnings was “depressingly familiar.”

“I see this time and time again in the cases I investigate,” he said, noting that a number of independent reports in recent years pointed to a defensive culture and hostility to those who disclosed safety issues.

Dr. Claudia Paoloni, an executive member of the hospital doctors’ union in Britain, said that the case followed a longtime pattern in which whistle-blower clinicians were ignored or victimized.

“Every single trust should be reviewing their existing systems to make sure they are robust and effective,” she said.

Dr. Jayaram said in his Facebook statement that there was a long history of whistle-blowers in the NHS, “not only being ignored but then being portrayed as the problem, sometimes to the point of their careers being destroyed.”

“What happened here was history repeating itself,” he wrote, “but the patient-safety issue that was ignored was beyond anything that the NHS has tried previously to cover up.”

The case has prompted calls for change.

Tamlin Bolton, a lawyer at Switalskis Solicitors, is representing the families of seven babies who were victims of Ms. Letby in civil claims against the Countess of Chester trust.

“We really need to look at what was known and what the trust knew during that timeline, to know what they could have done and what they should have done with what was presented,” Ms. Bolton said.

Immediately after the Letby verdict, the British government ordered an independent inquiry “to ensure vital lessons are learned and to provide answers to the parents and families impacted.”

But many experts, and representatives of the victims’ families, said this type of inquiry would not go far enough.

Mr. Behrens, the ombudsman, sent a letter to the health secretary on Wednesday calling for the government to set up a statutory inquiry, which would compel those involved to give evidence, rather than the weaker independent inquiry, which will allow people to opt out. He also requested better protection for whistle-blowers.

“This is a critical, pivotal moment in the history of our health service,” Mr. Behrens said. “And we need to understand why patient safety is not considered as important as the reputation of the trust.”