LONDON—The U.K. government is accelerating its vaccination drive as officials estimate that as many as three quarters of new Covid-19 cases in the country could be the result of a coronavirus variant first identified in India.

U.K. hospitalization numbers have ticked up and case numbers have risen 20% in the past week—though from a low base—as the variant takes hold in parts of the country, largely among younger people who haven’t yet received two vaccine doses.

“The latest estimates are that more than half and potentially as many as three quarters of all new cases are now of this variant,” the U.K. health secretary, Matt Hancock, said Thursday.