London — The coronavirus has been resurging across Europe, including in some places where it was thought to be well under control. A top world health official tells CBS News the trend shows that success today does not necessarily mean success tomorrow, and the United States should pay close attention.

Europe has seen a jump of more than 50% in new coronavirus cases over the last month, and the World Health Organization has warned the continent could see another half of a million deaths by February. CBS News senior foreign correspondent Charlie D’Agata spoke with the top official ringing those alarm bells, who told him there’s “grave concern” as Europe is once again under siege by COVID-19.

“If you look at the last four weeks, the hospitalizations have doubled,” Dr. Hans Kluge, the World Health Organization’s Regional Director for Europe, told CBS News.

He said vaccination uptake has plateaued in some parts of Europe and, “at the same time, there’s a relaxation of the public health and social measures, which is a cocktail for what we see: a fourth wave.”

Kluge called Europe “the epicenter” of a new global COVID-19 outbreak, fuelled by the highly transmissible Delta variant of the virus.

While case rates are up across the continent, European countries with higher vaccination uptake appear to be staving off a major new wave of severe COVID-19 illness, but in some Eastern European nations, the daily mortality rate is surging.

Portugal has one of the highest vaccination rates in the world, for instance, whereas Romania has one of the lowest in Europe — and one the highest death rates on the globe.

On Monday, Germany’s daily infection rate hit its highest recorded level since the pandemic began.

“Vaccines are a game changer,” said Kluge. But alone, they are “not enough.”

“We need to keep pressure on the virus, not surrendering on masks, the hand-washing, indoor ventilation — particularly in the schools,” he told D’Agata.

In the U.K., the virus’ spread in schools — where face masking and most other anti-virus mandates were dropped from the beginning of this academic year — is being blamed for rising case numbers. The rise, while not mirrored in hospitalizations or deaths, is stoking fear that another lockdown could be looming this winter.

“I think they can see it coming. But it’s that fine line between letting people go about their daily lives and also trying to keep people safe,” said Toni Watkins as she shopped on London’s Oxford Street, acknowledging the difficult calculous the British government and others across Europe are facing.

Kluge told CBS News that Americans should “absolutely” be paying close attention to the situation in Europe right now — and taking lessons from it.

“The basic principle is, if there is a situation where the peak is accelerating, don’t wait” to bring back anti-virus measures, and “the earlier, the stricter, the better.”

D’Agata asked Kluge what that could mean for the fast-approaching Thanksgiving and Christmas holidays. He said people should celebrate, but safely — trying to keep numbers down when different households mix, and he stressed the need to “vaccinate and ventilate.”