LONDON—Vikki Spit’s partner of two decades received his first Covid-19 shot in early May. Two weeks later, he died from a condition doctors for the 48-year-old former punk rock musician attributed to a rare vaccine side effect.

Ms. Spit now lives alone in a north England farmhouse, home to the couple’s rescue pets. Finances are tight. She struggles to maintain the online art-resale business her partner, who went by a single legal name, Zion, had started. She’s learning to drive—a task that had always fallen to him.

“Sometimes...

LONDON—Vikki Spit’s partner of two decades received his first Covid-19 shot in early May. Two weeks later, he died from a condition doctors for the 48-year-old former punk rock musician attributed to a rare vaccine side effect.

Ms. Spit now lives alone in a north England farmhouse, home to the couple’s rescue pets. Finances are tight. She struggles to maintain the online art-resale business her partner, who went by a single legal name, Zion, had started. She’s learning to drive—a task that had always fallen to him.

“Sometimes putting a kettle on seems more than I can manage,” she says. Ms. Spit is now among hundreds in the U.K. and elsewhere applying for government compensation for suspected injury caused by Covid-19 vaccines.

She is part of a very small, little-discussed community of pandemic victims: those who have suffered—or had family or loved ones suffer—from rare but serious vaccine side effects recognized by doctors, regulators and researchers. They say they feel lost in wider Covid-19 statistics, which have shown vaccines to be extremely safe and effective for most of the population.

“The problems are extremely rare,” said Kurt Weideling, whose wife, Nicola Weideling, 45, died in the spring in Southampton, England, from a condition doctors cited as a vaccine side effect. “That doesn’t make people any less dead.”

Faced with the gravest health crisis in memory, governments deployed newly developed vaccines in record time. Many countries indemnified pharmaceutical companies that made the shots, with some governments promising to consider compensation for suspected Covid-19 vaccine-related injuries.

‘Nicola was a big believer in vaccination,’ says her husband, Kurt Weideling.

Photo: Kurt Weideling

Now governments, including the U.S. and U.K., are trying to live up to that pledge. They are in the very early stages of applying existing vaccine-injury programs to hundreds of claims of injury alleged from Covid-19 shots.

Vaccine makers and health officials say risks from Covid-19 far outweigh risks of vaccination. Vaccines prevented more than a million deaths last year in the U.S. alone and more than 10 times that many additional Covid hospitalizations, according to an analysis by the Commonwealth Fund, a health-policy research foundation.

Serious side effects so far have been very rare—estimated at roughly one to 11 per 100,000 doses for some of the more serious harmful reactions identified by regulators in the most-affected age groups, according to U.S. and European government officials and researchers. They include blood clotting, nervous-system disorders and heart problems, all of which also can be caused by Covid itself.

Most of the side effects resolve quickly, but others in rare cases have required hospitalization and ongoing medical care. In even rarer instances, regulators and researchers tracking them say, side effects have been deadly.

One serious side effect is called “vaccine-induced immune thrombotic thrombocytopenia,” or VITT, linked to the shot co-developed by AstraZeneca PLC and the University of Oxford. Doctors for Ms. Spit’s partner and Mr. Weideling’s wife cited VITT after an AstraZeneca shot as the suspected cause of the conditions that led to their deaths.

The U.K.’s medicines regulator has received 438 reported cases of suspected VITT associated with the AstraZeneca shot. Of those suspected cases, 79 were reported to have been fatal. The U.K. leaned heavily on the shot in its vaccine rollout, administering more than 49 million AstraZeneca doses, among roughly 139 million doses the government has administered overall.

A photograph of Ms. Spit and her partner of two decades, Zion. She recalls when he went to the hospital: ‘I told him I loved him, and said I would see him soon.’ That was the last time she saw him conscious.

Photo: Mary Turner for The Wall Street Journal

Ms. Spit is waiting for a U.K. government decision about whether she can receive support from a program designed to help people or families who have suffered harm from a vaccine.

Photo: Mary Turner for The Wall Street Journal

“Individual vaccines will have different adverse events profiles, and people should be guided to identify early signs of adverse reaction so it can be appropriately treated,” AstraZeneca said in a statement. Oxford referred a request for comment to the AstraZeneca statement.

The U.K. government declined to comment about individual cases. June Raine, head of the U.K.’s primary medicines regulator, said in a statement that no vaccine is without risk, but that the shots’ benefits outweigh risks for most people. U.K. officials credit Covid-19 vaccines with saving more than 130,000 lives.

Researchers and public-health experts say it is difficult to measure global rates of rare adverse reactions to vaccines, especially in developing countries where monitoring is lacking. It is also harder to determine links between a vaccine and injury during a pandemic rampant with Covid-19 illness and untreated pre-existing conditions like heart disease.

Norway agreed to pay out 25 Covid-19 vaccine-injury claims as of early February. Three of those stemmed from deaths associated with the AstraZeneca vaccine and VITT, according to a spokeswoman. Of around 400 claims received so far, more than 300 are still being considered.

“The vaccines are new,” said Rolf Gunnar Jørstad, director of Norway’s agency handling the claims. A payout is appropriate if researchers have established a link between the adverse reaction and the vaccine, he said, and “there is no other probable cause or causes to the injury.”

The U.K.’s National Health Service has received more than 720 claims requesting Covid-19 vaccine-related compensation. The country’s vaccine-injury compensation program entails a one-size-fits-all cash payment of £120,000, equivalent to around $163,000. The volume of Covid-related claims has grown by about 20 a week, toward a projected 1,500 to 1,800 new claims this year, according to U.K. government projections.

“Ultimately these people were just trying to do the right thing,” said Gareth Eve, whose wife, Lisa Eve, a 44-year-old radio broadcaster who went by her given name, Lisa Shaw, died after a first dose of the AstraZeneca shot. An inquest ruled she died of complications from the vaccine, citing VITT. Mr. Eve has submitted a claim.

Lisa and Gareth Eve.

Photo: Gareth Eve

He went on to take three Covid-19 doses including a recent booster. “I just want people to be honest about what has happened,” he said. “There is always this caveat that, ‘But it has saved so many people’s lives.’”

U.S. health officials say nine people have died there from complications of thrombosis with thrombocytopenia syndrome, the name U.S. officials use for VITT, after receiving a Johnson & Johnson shot, out of more than 18 million J&J doses given. In 2020, the government added Covid-19 vaccines to an existing Department of Health and Human Services vaccine-injury program.

The program has received more than 3,320 Covid-19 vaccine claims, according to a spokesman. One claim has qualified for payment but isn’t completed. It relates to an anaphylactic reaction, or severe allergic response, to an undisclosed Covid-19 vaccine. The program “is working to process claims as quickly as possible,” the spokesman said.

Johnson & Johnson said it continues to collaborate with health experts to help healthcare professionals and the public know the risks of rare blood-clotting side effects, and recognize and treat problems quickly.

The vaccine developed by Pfizer Inc. and BioNTech SE, and the shot made by Moderna Inc. have been associated with a slightly elevated risk of inflammatory heart conditions myocarditis and pericarditis in a small number of cases, mostly among younger men.

Regulators and researchers have said that for most adults, the risks of heart complications from Covid-19 are much greater. Pfizer and Moderna said they continue to closely monitor safety data and share information with regulators and healthcare providers. U.S. health officials declined to comment on specific cases.

Matthew Wallick, a 38-year-old radiation therapist in Sacramento, Calif., was hospitalized in early January and diagnosed with myocarditis from a Moderna Covid-19 vaccine booster he received earlier the same week, according to medical records he provided. He still has mild chest pains and plans to file a damages claim, due within a year from the booster.

“I was never apprehensive about getting the vaccine,” Mr. Wallick said, adding his experience has made him feel that side effects still aren’t well understood. “This is part of the scientific process, in my opinion,” he said. “We are part of the scientific process.”

A vaccination clinic near the National Covid Memorial Wall in central London. U.K. officials credit Covid-19 vaccines with saving more than 130,000 lives.

Photo: tolga akmen/Agence France-Presse/Getty Images

Write to Jenny Strasburg at jenny.strasburg@wsj.com