The doubt, merited or not, around the AstraZeneca vaccines comes as more countries embrace or contemplate broad new restrictions — in some places for a third or fourth time in a year.

As of now, just about 8 percent of Europeans have received vaccines, even as new variants threaten to outpace and overwhelm the effort.

Short of widespread inoculations, and with the more easily transmissible and potentially more lethal British variant dominating infections, Italy extended tough new restrictions on movement nationwide on Monday, deepening a year’s worth of economic and psychic damage.

The quiet on the streets of Rome and elsewhere was eerily reminiscent of a year ago, when Italy became the first European country to shut down, underscoring to some how frustratingly little progress had been made in combating the pandemic.

“The second, the third wave, I have lost count,” said Barbara Lasco, 43, as she sat in a park in Milan, near the epicenter of the original European outbreak in northern Italy. “I am puzzled and disappointed; one year was enough time to keep this from happening again.”

Advances against the virus, nearly everywhere, have been maddeningly halting. In Germany, even as many nonessential stores opened last week for the first time in months, health officials called for caution.

“We are seeing clear signs: In Germany the third wave has already begun,” Lothar H. Wieler, the president of the Robert Koch Institute, Germany’s equivalent of the C.D.C. said on Friday. Since then, the daily numbers of infections have increased.

The virus is also spreading, and hospitals are again buckling, across Central Europe.

Prime Minister Viktor Orban of Hungary predicted that this week would be the most difficult since the start of the pandemic in terms of allocating hospital beds and ventilators, as well as mobilizing nurses and doctors.

In Germany, where infections are being driven by the British variant, a more lasting suspension of AstraZeneca could delay vaccination of the population by a month, according to the Central Institute for Registered Doctors.

France is hoping to stave off a new surge of infections with local restrictions, but some health officials think the time for a third national lockdown has come because intensive care units are swamped. “New decisions” will be taken in the coming days to tackle the rise in infections in France, Mr. Macron said on Monday.

Greek authorities last week reported the country’s highest daily rate of infections since mid-November, driven by the British variant; the rise prompted a reversal of plans to reopen schools and shops later this month.

Italy’s prime minister, Mario Draghi, warned on Friday that the country was facing a “new wave of contagion,” driven by more infectious variants of the coronavirus.

He has put an army general in charge of the vaccine rollout and hoped to increase inoculations from 100,000 a day to 500,000.

But that was before the AstraZeneca fears spread more widely.

On Monday, Iacopo Benini, a 32-year-old professor, had his AstraZeneca vaccination appointment canceled 20 minutes before he arrived for his shot in Milan. “Who is going to accept getting AstraZeneca now?” he said.

Reporting was contributed by Melissa Eddy and Christopher Schuetze from Germany; Constant Méheut and Aurelien Breeden from France; Emma Bubola from Milan; Matina Stevis-Gridneff and Monika Pronczuk from Brussels; Benjamin Mueller and Marc Santora from London; Benjamin Novak from Hungary; Niki Kitsantonis from Greece; Rebecca Robbins from Bellingham, Wash., Gaia Pianigiani from Siena; Thomas Erdbrink from Amsterdam; and Raphael Minder from Madrid.