According to the Our World in Data scientific aggregator, the rolling seven-day average of confirmed new cases per million inhabitants is on the rise in countries including Portugal, France, Germany, Italy, Spain, Greece, the Netherlands and Denmark.

Portugal has experienced the most dramatic wave, with infections per million remaining at a seven-day average of 2,043 on Monday – the second highest new case rate in the world, although down somewhat from an early June high of 2,878.

In France, the corresponding figure has soared from 224 on 13 June to 920 in the space of a week. “The pandemic is accelerating again, despite the warm weather,” Dr Benjamin Davido, an infectious diseases specialist at the Raymond-Poincaré hospital outside Paris, said.

“The new Omicron subvariants BA.4 and BA.5 are 10% to 15% more infectious and it’s this that is giving the virus an added kick,” Davido told French radio, adding that in the medium term the situation could become “very tough” in the country’s hospitals.

“We are in a very particular situation in which it is vital that we maintain stable immunity through booster shots.” Hospitals could fill up over the summer, he said, unless vulnerable people and those over 60 get a fourth dose as soon as possible.

Health expert Dr Damien Mascret told France 2 television that the BA.4 and BA.5 variants had led to significant excess deaths in Portugal, adding that hospital admissions in France were up 27% and intensive care admissions 17% in a week.

“The holiday season is about to start, almost all restrictions have been relaxed, things could take off again very fast indeed,” he said. “It’s concerning that only 29% of over-60s have so far got the fourth dose to which they are all entitled.”

The seven-day average infection rate per million is lower in Germany, reaching 715 on Monday, but has been climbing steadily since the first week of June when it stood at 324. The federal health minister, Karl Lauterbach, has spoken of a “summer wave” of new cases.

“This has unfortunately become a fact,” Lauterbach told the Rheinische Post newspaper last week, adding on Twitter that vulnerable people should get a fourth shot of the vaccine and suggesting masks were a good idea in enclosed spaces.

Germany’s BÄK medical association recently urged the government to prepare for an autumn and winter Covid onslaught, calling for extra planning to ensure schools stayed open, vulnerable people were protected and hospitals operated normally.

The Berlin government’s expert advisory council has said the country is benefiting from both a “high level of immunity” and variants causing relatively mild symptoms, but warned of a worst-case scenario in which hospitals could overwhelmed.

The combination of a more dangerous variant with rapidly waning immunity could pose serious problems, it said in a report, adding that masks indoors and capacity limits at major public events could soon be advisable, along with stricter measures in areas with more serious outbreaks.

Greece has also seen its seven-day average of new infections surge, from 377 per million on 13 June to 681 this week. The health ministry said on Monday cases would climb further, but it did not expect an increase in ICU admissions or deaths.

In Italy new infections have risen from 354 per million to 549 in the space of a week. ISS, the country’s national institute of health, said cases had climbed for the second week in a row, with the transmission rate rising again to epidemic level.

The percentage of infected patients in intensive care units continued to fall, but only one of Italy’s 21 regions is still considered a “low” risk, with 14 classified as “moderate” and the remaining six as “high” owing to the rising number of alerts.

Prof Walter Ricciardi, a former president of the institute, told Adnkronos that the government may have relaxed restrictions too quickly. “It’s our third summer (of the pandemic) and we still haven’t learned our lesson,” Ricciardi said.

Case numbers in the Netherlands have risen for a third week in a row, the Dutch public health institute, RIVM, said on Tuesday, blaming the global rise of the BA.4 and BA.5 subvariants. According to Our World in Data, the Dutch seven-day infection rate has surged from 117 per million to 204 per million in the past week.

The two biggest Dutch employers’ organisations called on Monday for people to return to observing basic coronavirus hygiene rules, saying a new wave appeared imminent, while the health minister, Ernst Kuipers, has said there was a “very real” risk of millions of people becoming infected this autumn.