(Updates rising UK, Belgian and U.S. figures)

* Anti-restriction protests turn violent in Italy

* France warns of "difficult decisions" ahead

* Trump pushes vaccines, but none yet available

ROME, Oct 27 (Reuters) - European governments moved on Tuesday to impose new curbs to try to contain a rapid surge in coronavirus infections and provide economic balm to help businesses survive the pandemic.

World leaders face an increasingly difficult task as they seek to limit the spread of the disease and the damage to their economies, while they pin their hopes on as-yet unproven vaccines.

"We are dealing with exponential growth," German Economy Minister Peter Altmaier told a virtual German-French economic conference in Berlin. "In Germany, the number of new infections is rising by 70-75% compared to the week before."

France, Poland, Russia, Sweden, the United States and other countries have registered record numbers of infections in recent days as autumn turns to winter in the Northern Hemisphere and people socialise indoors where the risk of infection is higher.

More than 43.4 million people have been infected by the coronavirus globally and 1,158,056 have died, a Reuters tally found. The United States has the highest number of infections and deaths.

Hundreds of protesters took to the streets across Italy on Monday to vent their anger at the latest round of restrictions, including early closing for bars and restaurants, with demonstrations in some cities turning violent.

In the financial capital Milan, youths hurled petrol bombs at police, who responded with volleys of tear gas. In nearby Turin, luxury shops had their windows smashed and some were ransacked, leading to the arrest of 10 rioters.

In France, Interior Minister Gerald Darmanin told the country to prepare for "difficult decisions" after some of the strictest restrictions in place anywhere in Europe have failed to halt the spread of the disease.

The United Kingdom recorded a further 367 deaths within 28 days of a positive COVID-19 test on Tuesday, the highest daily toll since May 27, government data showed.

The Czech government will ask lawmakers to extend its emergency powers until Dec. 3, Prime Minister Andrej Babis said on Tuesday, as it tries to stem one of the strongest surges in infections in Europe.

BRAIN FUNCTION AFFECTED

There have been at least 8.54 million reported infections and 251,000 deaths caused by coronavirus in Europe so far, the latest Reuters data shows. The continent registered a record 230,892 new cases on Monday, up from 67,739 on Oct. 1.

Authorities in Russia, which with 1.55 million infections has the world's fourth largest coronavirus case load, ordered people to wear facemasks in some public places and asked regional authorities to consider shutting bars and restaurants overnight.

The Belgian government will convene on Friday to decide on a potential national lockdown as the country suffers the highest EU rate of coronavirus infections per 100,000 citizens, official data show.

Even Germany, widely praised for its initial response to the pandemic, signalled concern on Tuesday over rising infections, with Altmaier saying the country was likely to reach 20,000 cases a day by the end of this week.

Spain's wine-producing region of La Rioja ordered the closure of restaurants and bars in its two largest towns for a month. A nationwide curfew has been in place since Sunday.

A gauge of global stock markets fell and the U.S. dollar slipped on Tuesday as investors grappled the rise in coronavirus cases and uncertainty over the impending U.S. election.

Adding to the gloomy sentiment, a new study by Imperial College London found that antibodies against the new coronavirus declined rapidly in the British population during the summer, suggesting protection after infection may not be long-lasting. Recovering patients may also suffer a decline in brain function, researchers said.

In the United States, the number of hospitalised COVID-19 patients is at a two-month high, straining health care systems in some states. The U.S. death toll is the highest in the world at more than 225,800.

Nearly half a million people in the United States have contracted the virus in the last seven days, a Reuters tally found.

"Until November 4th., Fake News Media is going full on Covid, Covid, Covid," President Donald Trump, facing a tough re-election battle on Nov. 3, tweeted on Tuesday in an often-repeated refrain without offering evidence. "We are rounding the turn. 99.9%."

Trump has often promoted vaccines as the answer, but none has yet won international approval. Russia in August became the first country to grant regulatory approval for a vaccine after less than two months of human testing, raising eyebrows among sceptical scientists in the West.

A vaccine being developed by the University of Oxford and AstraZeneca Plc produces an immune response in both old and young adults, the company said on Monday, raising hopes of a path out of the gloom.

(Reporting by Reuters bureaux; Writing by Crispian Balmer and Nick Macfie; Editing by Alison Williams, Jon Boyle and Barbara Lewis)