LONDON — Britain on Tuesday surpassed 100,000 deaths from the coronavirus, a tragic milestone that laid bare the missteps in Prime Minister Boris Johnson’s handling of the pandemic, as well as the tough choices he now faces in trying to keep lethal new variants of the virus out of the country.

Britain’s death toll has long been the worst in Europe, but a fast-spreading variant of the virus has propelled the country’s daily fatality rates to levels not seen since the peak of the pandemic’s first wave in April, despite a national lockdown. Per capita, Britain’s death rate has been the worst in the world over the last week.

“It’s hard to compute the sorrow contained in that grim statistic,” a solemn Mr. Johnson said of the death toll, which hit 100,162. “You’d exhaust the thesaurus of misery. It’s an appalling and tragic loss of life.”

Mr. Johnson had been expected to discuss a mandatory hotel quarantine for travelers arriving in Britain from countries with dangerous outbreaks of the virus. But the details of that plan were not yet settled, attesting to both its far-reaching economic implications and the logistical challenge of housing, feeding, and monitoring thousands of passengers landing at British airports.

Tighter travel restrictions would aim to keep new variants from Brazil and South Africa out of Britain. Among the proposals under consideration is one that would require travelers from South Africa, South America and Portugal to quarantine in hotels for 10 days after arrival.

That would push Britain in the direction of Australia, which has used hotel quarantines in a mostly successful effort to keep the virus outside its borders. But Britain would be acting months later than Australia and after the spread of its homegrown variant has already swamped hospitals.

Speaking to reporters at Downing Street, Mr. Johnson declined to dwell on the mistakes that, in his government’s handling of the crisis, worsened the death toll. As several reporters reminded him, the government once said that keeping the death toll to 20,000 would count as a success.

“I am deeply sorry for every life that has been lost,” Mr. Johnson said, adding that he accepted responsibility. “We truly did everything we could, and continue to do everything we can, to minimize loss of life.”

Mr. Johnson’s chief medical adviser, Chris Whitty, was more reflective, acknowledging that some issues could have been better handled. In the early days of the pandemic, he said, experts did not properly appreciate the importance of face masks, nor did they understand sufficiently the significance of asymptomatic transmission. As the crisis has ground on, Mr. Whitty said, the medical profession has developed new and improved ways of treating Covid patients.

For Mr. Johnson, the pandemic has become a grim race between vaccinating the population and holding off new variants, which could fuel another surge in infections. On the vaccine front, Britain continues to make major strides, injecting 6.8 million people, the fastest pace of any large country.

But in other respects, the government still appears late and disorganized. On the travel plan, some health experts argue that anything short of a blanket hotel quarantine would not be effective. But critics say the government would not be able to handle the logistical challenge, as arriving passengers would quickly fill up the hotels around London’s Heathrow Airport, the country’s main gateway.

Britain’s plans come as the United States has moved to tighten restrictions on overseas visitors. President Biden rescinded an order by former President Donald J. Trump that would have relaxed travel bans on non-Americans from Britain, Brazil, South Africa, and much of the European Union.

The new U.S. rules, which took effect Tuesday, led to confusion at Heathrow Airport as British Airways turned away U.S.-bound passengers. That included even some who met the updated guidelines set by the Centers for Disease Control, which stipulate that they either had to produce a negative coronavirus test or a doctor’s letter confirming that they had recovered from Covid and were no longer infectious.

For the travel industry, the quarantine would be the latest in a succession of blows that has cost tens of thousands of jobs and driven some companies, like the cross-Channel train operator Eurostar, to the financial brink.

“It will be another nail in the coffin of the travel industry,” said Steven Freudmann, the chairman of the Institute of Travel and Tourism, which lobbies for the sector. “The industry understands the motives and we put the health of the nation first, but what is so frustrating is that the rules are changing literally week by week.”

In Britain, “closing the doors appears to us to be happening 12 months too late,” Mr. Freudmann said, adding that the move would further erode confidence at a time when the sector was starting to plan for recovery.

Even those traveling to and from countries not deemed high risk will worry that the risk status of those nations might change without warning while they are away. And, though some hotels might benefit from accommodating quarantining passengers, that would be a short-term gain.

“Who wants to come knowing they have to spend 10 days in a hotel and pay for the privilege?” Mr. Freudmann said.

Britain’s travel policy has been marked by twists and turns from the start. The government initially argued that restrictions would make little overall difference given that the virus was already circulating in Britain.

Then in July, when it moved abruptly to introduce a quarantine on travelers from Spain, it embarrassed the minister responsible for aviation policy, the transport secretary, Grant Shapps, who learned of the decision while he was on vacation — in Spain.

Under the rules in place last summer, travelers from a range of lower-risk countries were exempt from the requirement to isolate themselves. But the list was reviewed each week, making the decision to travel a gamble for vacationers, thousands of whom found themselves abroad while changes came into force.

Britain was slow to introduce requirements on travelers to show a negative coronavirus test result and, when it did so recently, struggled to provide enough staff to check those arriving, causing crowded scenes in some airport arrival halls.

Some critics argue that the problem with the British system is lackluster enforcement, not just of quarantining travelers but of Britons asked to stay home after testing positive for the virus, or being in contact with someone who had.

“The elephant in the room here is the number of people domestically who we need to be self-isolating who aren’t — and we’ve really got to address that,” the former health secretary, Jeremy Hunt, told Sky News.