Italy’s government-run statistical agency on Wednesday reported a nationwide jump in deaths for the first three weeks of March from a year earlier—particularly in northern Italy, where it found the number of deaths more than doubled in over half the hundreds of towns and cities it surveyed.

“If you base any policy-making on these numbers, you should be very careful,” says Lucas Böttcher, a researcher at the University of California, Los Angeles, who has modeled fatality rates for Covid-19. “They can highly fluctuate during an outbreak.”

Nowhere in Italy has been harder hit than Bergamo, a city of about 120,000 people. In March 2019, 125 people died in the city. This March, 553 people died. Of these, 201 deaths were officially attributed to the virus. This leaves 352 further deaths for the period, far higher than normal.

In the wider Bergamo province, which comprises the city and more than 240 small towns and has a total population of 1.1 million, 2,060 people died in March from the virus, according to the official count. But some 4,500 more people died in the province in March than a year earlier, according to a new joint study by the local Eco di Bergamo newspaper and research firm InTwig that took data from 91 towns in the province.

The real number of deaths in the province of Brescia, where this funeral was conducted, appears to be at least double the official count of 1,278 since the outbreak began in late February.

“Other countries that have the good fortune to be seven to 14 days behind us have to use that time to erect defenses,” says Giorgio Gori, Bergamo’s mayor, who estimates the virus has spread so widely in his city that one-third of the population has been infected. “We were first, and we weren’t prepared. Any leaders looking at us and not reacting vigorously will have a lot to answer for.”

Similar situations have played out across the Lombardy region, which accounts for 58% of Italy’s official coronavirus deaths.

In towns around Lombardy, local officials and doctors say the deaths recorded in March are many times the average monthly number. Often, the monthly toll matches deaths that towns normally record over half a year.

The health-care system in the region is so overstretched that doctors can’t treat all the sick. Those who die outside the hospital usually aren’t tested for the coronavirus.

“They are not receiving postmortem tests,” Eleonora Colombi, a family doctor based near Brescia, says of people who die outside hospitals, such as in nursing homes. “Many of those who die and aren’t tested are old, but you normally don’t have so many people all dying at the same time. It’s corona.”

At Dr. Colombi’s office, three patients who tested positive for the coronavirus have died in recent weeks. But an additional 20 people who died with symptoms associated with the virus weren’t tested.

The problem isn’t just with patients sick with Covid-19.

“We have a problem with the elderly and other sick people like cancer patients who are dying at home,” says Dr. Colombi. “The ambulance won’t come if you are 94 years old and there are 50 other people waiting.”

An added problem is that 20% of Bergamo’s family doctors have been infected—and those still working only consult with patients over the phone. The local health service has responded to the high infection rate among family doctors by instituting teams of three to four doctors that make house calls in full protective gear. But with only eight teams for all of Bergamo, and each team able to make only about eight visits a day, many people don’t receive care.

So many coffins are accumulating that they are being stored in warehouses like this one in Ponte San Pietro, near Bergamo.

Pietro Fiore, the mayor of Castellone, a small town south of Milan, says some local residents have died because they weren’t brought to the hospital for conditions that might have been treatable because the hospitals were overwhelmed with coronavirus patients.

In Castellone, 31 people died between March 1 and March 26, compared with five in that period last year. About eight of the 31 deaths were officially attributed to the coronavirus, but about 10 more were probably caused by the virus, and a similar number by potentially treatable ailments, says Mr. Fiore.

With Italy under a strict lockdown, it isn’t only funerals that have become impossible. In Castellone, death notices aren’t being posted on billboards around the main piazza, as is often done in small Italian towns. In Castellone, where the tradition is still strong, residents normally follow up the death notices with their own notices posted around the town expressing condolences for the families of the deceased.

“People don’t even know who is dying, and there isn’t the chance to show support for the families that lose people,” says Mr. Fiore. “That’s the hardest thing.”

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There are signs the lockdown that was imposed on March 8 across Lombardy and two days later on the whole of Italy is beginning to have an effect. The rate of contagion has slowed, and fewer people are being admitted to the hospital. A study by a team of epidemiologists at Imperial College London estimates that Italy’s strict social-distancing measures prevented about 38,000 deaths up to the end of March.

It will take time for the number of daily deaths to come down, since many of those who are dying became infected weeks ago. For now, the sheer number of people dying is still overwhelming Italian towns. Funeral-service agencies that work with hundreds of funeral homes in Brescia and Bergamo say the number of dead they buried or cremated in March was more than twice the number in March last year. The stated cause of death is often just pneumonia, without reference to the coronavirus, they say.

In Bergamo, so many coffins were accumulating in mid-March that a convoy of army trucks came to take them away for cremation elsewhere. In Brescia, the local diocese has offered 40 empty churches to store coffins as they await their turn for cremation, which can sometimes take up to two weeks. While funerals aren’t allowed because of social-distancing requirements, priests still bless the dead.

“One of the most difficult things to accept is that unfortunately many people are dying on their own, with none of their dear ones next to them,” says Brescia Bishop Pierantonio Tremolada, who gives regular blessings over the coffins in churches. “That is something we can still do for them.”