England will overhaul its faltering coronavirus contact-tracing system, the government said on Monday, shifting some control from private contractors to local public health teams and cutting the jobs of thousands of call center workers who had complained of having no one to call.

The changes were the clearest acknowledgment yet by British Prime Minister Boris Johnson’s government that its centralized, privatized system for tracking down the patients’ contacts has come up short.

Instead, the government has heeded some of the pleas of underfunded local public health directors, who have been warning for months that a London-run contact tracing system would not deliver the local intelligence needed to squelch flare-ups of the virus.

Under the reorganization announced on Monday, 6,000 contact tracing jobs will be cut by late August, one-third of the total employed by two outsourcing companies. Some of the remaining 12,000 privately employed tracers will be redeployed to regional public health teams.

In some areas, “the national Test and Trace system wasn’t picking up enough of the cases and contacts on the ground to make a difference,” Dr. Lincoln Sargeant, the director of public health in North Yorkshire, said in an interview on Monday. “The knowledge and relationships we have in local government are certainly what you need to bridge that gap.”

Contact tracing has long been envisioned as the bridge between lockdown and a vaccine, allowing the government to identify clusters of infections and stop people from passing on the virus. Without an effective system, scientists warned recently, schools could not safely reopen in September, as planned.

But England’s centralized program has repeatedly stumbled since its rushed launch in late May — one of many missteps that have contributed to Britain’s having the worst outbreak in Europe.

Only 51,500 of the 92,000 people identified as close contacts of positive cases were ever reached by call center contact tracers as of late July, according to government statistics. Many contact tracers had reached no more than a couple of people in two months of work.

Contact tracers reported filling their days with Netflix and internet exercise classes. Local public health directors struggled to get access to testing data from their areas. Outbreaks sprouted in cities like Leicester, necessitating economically damaging local shutdowns.

Part of the problem, analysts said, was that Mr. Johnson had entrusted England’s system largely to Serco, an outsourcing giant that had recently been obliged to pay the government a hefty fine for fraud on a previous, unrelated contract. Other nations within the United Kingdom, including Wales and Scotland, which are in charge of their own contact tracing, appointed public health officials to run their programs.

The callers employed by Serco and other outsourcing companies were paid barely above the minimum wage, and some said they started work with little or no training.

Small teams of local public health workers employed by local authorities picked up the most complicated cases in settings like nursing homes, schools, homeless shelters and prisons. They traced more contacts than the privately employed workers, and reached a higher percentage of them: By late July, they had reached 148,000 of 151,000 contacts.

In redeploying more contact tracers to those local teams, the government is hoping to replicate that success more broadly. Rather than stopping once they fail to reach people by phone, tracers will now work with public health officials to take further action, like knocking on people’s doors.

“N.H.S. Test and Trace is one of the largest contact tracing and testing systems anywhere in the world, and was built rapidly, drawing on the U.K.’s existing health protection networks, to stop the spread of coronavirus,” Dido Harding, the executive chair of the program, said in a statement on Monday. “We have always been clear that N.H.S. Test and Trace must be local by default and that we do not operate alone.”

The government did not say how it would handle its 108 million pound, or $141 million, contract with Serco. The government has until late August to decide whether to expand the contract to up to $535 million.

Local public health directors said that bringing the London-run system under the umbrella of regional health authorities could create difficulties with merging records. They said it would be important to ensure that national and local systems do not replicate each other’s work.

But public health officials said involving local authorities may make people more amenable to following official guidance. Several areas have already undergone trials with the new system.

For one thing, they said, people seemed more likely to pick up calls that came from local area codes. Local authorities are also largely responsible for trying to secure help for people who lack the housing, income, savings or access to food that would allow them to isolate for two weeks.

Still, England is offering less support than some countries with more successful contact tracing systems. In Germany, for instance, people who have to quarantine continue to be paid their regular wages for a period. In China, people asked to isolate at home have their rent and food paid for by the government.

In England, many people in insecure employment may not be paid at all or risk being fired if they have to stay home from work. Others cannot afford to live on the allocated sick pay.