LONDON — In the first study to describe the nationwide effectiveness of two vaccines, researchers in Scotland reported Monday that both the first doses of the Pfizer-BioNTech and Oxford-AstraZeneca shots greatly reduced hospital admissions for covid-19 among the elderly — changing by up to 85 percent and 94 percent, respectively.

British public health officials hailed the results from the “real-world” studies, which are showing that the vaccines are beginning to have a positive impact in the coronavirus pandemic. Arne Akbar, president of the British Society for Immunology, called the initial data “extremely promising.”

The Scottish researchers analyzed a data set covering the entire Scottish population of 5.4 million, of which 1.1 million people — about 20 percent of the population — have received a first dose of the Pfizer or Oxford vaccines. Then, they compared the vaccinated with the unvaccinated, and they saw strong evidence of protection.

From December until the middle of February, more than 8,000 people ended up in the hospital with covid-19 in Scotland, but only 58 of those patients came from the vaccinated group.

Combining results for both vaccines for people 80 and older, there was an overall 81 percent reduction in hospital admissions by the fourth week, said Aziz Sheikh, professor of primary care research and development at the University of Edinburgh and one of the principal investigators.

Sheikh cautioned that the immunity offered by the first doses of the vaccines could wane. But more will be known as researchers follow the vaccinated after their second doses.

Josie Murray of Public Health Scotland, another leader in the study, told journalists “the other fantastic news” is that the vaccines should already be helping reduce the covid-19 burden on National Health Service hospitals.

In its initial rollout, the vaccine campaign in the United Kingdom prioritized nursing home residents, health-care workers and all those over age 70, who are most at risk of severe illness, hospitalization and death from covid-19. Britain is now asking all those over 65 to roll up their sleeves.

Previous results about vaccine efficacy have come almost exclusively from clinical trials. The first population-level studies have been reported from Israel. They looked at the effectiveness of just one vaccine, Pfizer-BioNTech, which has been shown to be almost 96 percent effective in preventing hospitalizations and death. Israel has vaccinated almost half its adult population.

The Scottish research was released in a preprint Monday and is not yet peer-reviewed. In a statement, the co-developer of the Oxford vaccine, Sarah Gilbert, said the high effectiveness in protecting those over 80 after a single dose increases “confidence in using this vaccine in adults of all ages.”

In a second study, also released Monday, Public Health England scientists presented preliminary data showing that the Pfizer-BioNTech vaccine appears to provide high levels of protection not only against symptomatic covid-19 but against coronavirus infection.

Researchers have been examining a cohort of vaccinated health-care workers every two weeks — whether they have covid-19 symptoms — and they found that one dose reduced the risk of infection by more than 70 percent, rising to 85 percent after the second dose.

“This suggests the vaccine may also help to interrupt virus transmission, as you cannot spread the virus if you do not have infection,” the PHE researchers said in a statement.

Alongside these encouraging results, Prime Minister Boris Johnson outlined the next steps Monday in lifting the country’s national lockdown, a “road map” that he said he hopes will be “cautious but also irreversible.”

It will be a slow march, Johnson warned.

He outlined detailed plans in Parliament, telling lawmakers that there would be four stages, with a minimum of five weeks between each stage. The earliest possible date that most of the restrictions could be lifted is June 21, the prime minister said.

The first big changes will occur March 8, when all schools in England will reopen, two people from different households will be able to meet outdoors and nursing home residents in England can receive one regular visitor. In April, hair salons, barbers, gyms and nonessential shops may open. In May, pubs and restaurants. In June, foreign holiday travel could resume.

The British government is being far more tentative about easing restrictions this time, even as its vaccination rollout is going astonishingly well — about a quarter of the population has had at least one shot of the vaccine.

The new changes will be rolled out slowly. At each stage, the government says its decisions will be driven by data — figures on the vaccine rollout program, hospital admissions and deaths, infection rates and the impact of any new variants.

The semiautonomous governments in Scotland, Northern Ireland and Wales have their own timetables.