LONDON—Britain announced on Tuesday 1 billion pounds ($1.3 billion) of extra support for businesses hit hardest by the wave of Omicron variant coronavirus cases, which is hammering the country’s hospitality sector and other businesses. Finance minister Rishi Sunak said he was confident the measures would help hundreds of thousands of businesses. But he added that he would “respond proportionately and appropriately” if the government were to impose further restrictions to slow Omicron, which would further hit the economy. Under the support announced on Tuesday, hospitality and leisure firms in England will be eligible for grants of up to 6,000 pounds for each of their premises, accounting for almost 700 million pounds of the new package. The grants were equivalent to those provided to hospitality businesses when they were fully closed earlier this year, the finance ministry said. A fund to support cultural organisations would be increased by 30 million pounds, …