CNN  — 

The United Kingdom and France both reported their highest rise in daily coronavirus case numbers Thursday with Europe in the grip of a second wave of infection.

It comes amid a flurry of outbreaks at universities across Europe, which has seen students in Scotland toldthere must be no parties, and no socialising outside their households.”

French health authorities reported 16,096 new Covid-19 cases in 24 hours. A total of 31,511 people have died from coronavirus in France, and 497,237 cases have been reported.

The UK reported 6,634 new cases, bringing its total confirmed cases to 416,363, Public Health England (PHE) tweeted.

“This is the highest number recorded and a stark warning for us all. The signals are clear. Positivity rates are rising across all age groups and we’re continuing to see spikes in rates of admission to hospital and critical care,” said Public Health England medical director Yvonne Doyle.

Visitors stand in line at a coronavirus walk-in testing center in Edmonton, London, on Wednesday.

Forty more deaths were reported in the UK Thursday and its death toll, according to PHE, now stands at 41,902 – Europe’s highest.

Spain’s Ministry of Health reported 12,272 new Covid-19 cases Friday, bringing the total to 716,481. Madrid’s region reported 213,709 cases, almost 30% of the country’s total.

Spanish Health Minister Salvador Illa said Friday his government has recommended a total lockdown in the capital. “I think we have difficult weeks to come for Madrid and we need to act decisively,” Illa said.

The Czech Republic reported 2,913 new infections Friday, its second-highest daily increase. Germany’s case number rose by 2,143 to 278,070 Thursday, according to data from the country’s infectious disease agency, the Robert Koch institute. While this is well below its record of almost 7,000 daily cases in early April, case numbers are still on an upward trajectory – and Germany was one of the few countries to have widespread testing early in the pandemic.

Customers crowd a Parisian cafe Wednesday as the French government announced that from Monday all bars in the city will shut at 10 p.m.

The surge comes as thousands of students across Europe began self-isolating following outbreaks of Covid-19.

All 2,500 students at Ecole hôtelière de Lausanne, Switzerland’s most prestigious hospitality school, are quarantining after outbreaks linked to “one or more parties,” the Vaud Canton regional authority said Wednesday.

Several Scottish universities reported Covid-19 outbreaks linked to illicit gatherings during start of term celebrations known as “Freshers’ Week.”

Staff from the UK's National Health Service (NHS) hand out test kits to Glasgow University students as they arrive at a pop up test center at the Murano Street Student Village residence.

On Wednesday, 600 students at the University of Glasgow were told to self-isolate after 124 new cases were confirmed. The University of St. Andrews, one of the UK’s most elite colleges and Prince William’s alma mater, asked students to go into voluntary lockdown last Friday after an uptick in cases that it linked to one party.

Meanwhile, UK grocery giant Tesco on Friday announced three-item limits on essentials including flour, dried pasta, toilet roll and antibacterial wipes, to avoid the panic-buying that caused shortages in spring.

A spokesperson said: “We have good availability, with plenty of stock to go round, and we would encourage our customers to shop as normal.”

Europe under pressure

Drinkers at the Westminster Arms pub in London watch as British PM Boris Johnson makes a televised address to the nation on Tuesday.

There are 6,031 people in hospital with coronavirus in France, the highest number since July 22, including 1,048 people in intensive care units. A total of 1,048 contagion clusters are under observation (up 11 in 24 hours).

The Paris public hospitals authority announced it will start canceling some non-elective procedures in coming days to make room for coronavirus patients, although it said it would be on a case-by-case basis and not “global cancellation as in mid-March.”

While Europe’s dramatic rise in cases is partly explained by greater testing capacity, many countries are also seeing a higher percentage of tests coming back positive, according to health experts.

The continent reported a record 55,270 new daily cases on a seven-day rolling average Thursday, but just 550 new deaths, according to CNN analysis of Johns Hopkins University figures. Hospitals and individuals are now better prepared to cope with the virus, but there are fears deaths could rise as the colder weather and flu season arrive.

The EU’s Health Commissioner warned that Europe is at a “decisive” point in dealing with its second wave, and the actions taken now will determine the severity of restrictions needed in the coming months.

Italy, the worst-affected European country early in the pandemic, reported a relatively low increase of 1,786 new cases Thursday, but its health minister cautioned: “The situation in Europe is serious and cannot be underestimated.

“I believe that we must keep our feet on the ground and continue to invest in the line of prudence.”

CNN’s Amy Cassidy, Niamh Kennedy, Nadine Schmidt and Livia Borghese contributed to this report.