LONDON — Britain's fast-running coronavirus vaccination campaign appears to have hit its early target, offering a first dose to 15 million elderly people and health-care workers by Monday, as the government promised.

Prime Minister Boris Johnson hailed the National Health Service for nailing the deadline, calling the rapid rollout of two vaccines an “unprecedented national achievement,” but also warned that now was “no moment to relax.”

The British government has been promoting its vaccine numbers hard, while it faces criticism for other aspects of its response. Britain has one of the highest death tolls in the world.

Most of those who have received the vaccine have received only one dose of the two needed to achieve the full effect. The first doses were offered to all those older than 70, alongside nursing home residents, caregivers, front-line medical workers and those with serious illnesses that might make them more vulnerable to covid-19, the disease caused by the coronavirus.

Despite early fears about vaccine hesitancy, a spokesman for 10 Downing Street called the takeup “very high.” Like the United States, Britain has a small but vocal anti-vaccine community. Many of the hesitant, however, have told pollsters that they are taking a “wait-and-see” approach vs. outright refusing the shots.

Britain leads Europe on vaccine deployment per capita, and trails only smaller countries, such as Israel and the United Arab Emirates, worldwide.

The quick rollout, combined with the high uptake, is clearly a win for the Johnson government. Britain has been plagued with problems as it confronts the coronavirus, and on many days it has suffered the highest death toll from the virus in the world. The country is in its third national shutdown, with all schools and universities closed and stay-at-home orders enforced by fines.

Uptake has surpassed expectations, officials said. Infectious-disease analysts anticipated 75 percent participation, said Simon Stevens, the chief executive of NHS England. But uptake among those 70 and older has been almost 90 percent, Health Secretary Matt Hancock said Monday. Among people ages 75 to 79, he told the BBC, “over 97 percent have taken up the offer.”

Participation among residents of hard-hit nursing homes who were “clinically eligible” for the vaccines has been more than 90 percent, Hancock said.

Within the National Health Service, takeup has been 80 percent for health-care workers at doctor’s offices and hospitals, he said. That’s considerably higher than for seasonal flu vaccines for medical workers. Last year, 74 percent of NHS front-line medical staff members received a flu shot, but in previous years it was about 60 percent.

One group that appears to be lagging is low-wage workers who care for residents of nursing homes. The health secretary reported that about two-thirds of the staff members who work in social care had received their first dose.

Johnson’s government insists that vaccines will never be mandatory, even for health-care workers. Officials want all of them to take their doses voluntarily.

But some nursing homes have begun to insist on a shot. Barchester Healthcare, a private provider that runs more than 200 homes nationwide, says it has changed its hiring policy. “New staff have to have been vaccinated,” if they medically can, a spokesman said, “but this does not currently apply to existing staff.”

Johnson wants all those 50 and older — alongside all other risk groups — to be vaccinated by April. Then the government will tackle the rest of the population. Already, general practitioners are texting, calling and writing to urge those in their 60s to make appointments.

Britain changed its strategy at the start of the new year to reach more people by delaying the second dose by up to 12 weeks after the first. The previous interval was three weeks.

British regulators have approved the Pfizer-BioNTech and Oxford-AstraZeneca vaccines for emergency use. A third, made by Moderna, has been approved but won’t be administered until the spring.

Analysts have expressed concerns about disparities between White Britons and Black, Asian and minority ethnic (BAME) communities.

One study, not yet peer-reviewed, found significant disparities in vaccine uptake among health-care staff members of different ethnicities at NHS University Hospitals of Leicester. Leicester is one of the most ethnically diverse cities in Britain. More than 19,000 staff members have been offered a vaccine. Researchers found that 71 percent of White staff came forward to get a shot, compared with 59 percent of South Asian staff and 37 percent of Black staff.

University of Leicester professor Kamlesh Khunti, one of the authors of the study, tweeted: “Urgently need to identify barriers & overcome these.”

Nadhim Zahawi, Britain’s vaccine minister, told Sky News that those not taking the vaccines “skew heavily toward BAME communities.” “If one particular community remains unvaccinated,” he said, “the virus will seek them out and it will go through that community like wildfire.”

Public health analysts said uptake in some BAME communities, which include immigrants, might be affected by issues of trust and misinformation. There are also concerns that a number of young people might not want to take the vaccine.

“Older people are more likely to get the vaccine, partly because they are at high risk, and also because they have had a prolonged period of lockdown,” said Martin Marshall, chairman of Royal College of General Practitioners. “Many [have] not been out in a year, desperate to go out to see friends. Likely we’ll see a lower uptake in younger people, but we don’t know for sure yet.

To beat the pandemic, it’s not enough for the world’s top scientists to develop an effective vaccine in record time. People need to take it.

“The more people who have [been] vaccinated, the higher chance you have of the virus not circulating,” Marshall said. “If young people don’t accept the vaccine, it could potentially be a problem because there will be more people susceptible, and a larger reservoir for the virus to continue circulating.”

Azra Ghani, chair of infectious-disease epidemiology at Imperial College London, advised focusing on two numbers: the vaccines’ efficacy rates and how many people take them.

“Uptake is as important as vaccine efficacy” in slowing the spread of the virus, she said.

It’s especially worrisome if the uptake is low in clusters in individual communities, giving the virus an open field to spread.

Paul Hunter, a professor of medicine at the University of East Anglia, said vaccinations alone may not be enough to stop the coronavirus.

“If you’ve been vaccinated, and if you can still get infected and infect other people, then you will not achieve herd immunity,” he said. But he said it was right for Britain to prioritize the most vulnerable, because the vaccines have been proved effective at stopping people from becoming severely ill and dying.

“The dangerous time for people is getting their first-ever infection with no prior immunity and in a vulnerable category. The critical thing is protecting those people so they don’t die when they first get the infection.”

He said the virus isn’t likely to disappear, but might be made manageable. “Our grandchildren’s grandchildren will be getting covid, but by then, or probably a lot sooner, it won’t be much different than the common cold.”