LONDON — Pubs and restaurants across much of the U.K. opened for indoor service for the first time since early January on Monday, even as the prime minister urged people to be cautious amid the spread of a more contagious COVID-19 variant.

The latest step in the gradual easing of nationwide restrictions imposed on Jan. 4 also includes the reopening of theaters, sports venues and museums, raising hopes that the economy may soon start to recover from the devastating effects of the pandemic. The government is also relaxing guidance on close personal contact, such as hugging, and permitting international travel, though only 12 countries and territories are on the list of “safe” destinations.

But the rapid spread of a variant first discovered in India is tempering the optimism amid memories of how another variant swept across the country in December, triggering England’s third national lockdown. Public health officials and the government are urging people to continue to observe social distancing and hygiene guidance, even though they say the situation is different now because almost 70% of the adult population has received at least one dose of vaccine.

“Please, be cautious about the risks to your loved ones,’’ Prime Minister Boris Johnson said in a video posted on Twitter. “Remember that close contact such as hugging is a direct way of transmitting this disease, so you should think about the risks.”

Britain has Europe's highest coronavirus death toll, at some 128,000 people.