Alarmed by the coronavirus variant spreading in Britain, Gov. Andrew M. Cuomo of New York announced on Monday that British Airways, Virgin Atlantic and Delta Air Lines have agreed to require a negative coronavirus test result from passengers boarding flights from Britain to New York.

Gov. Jay Inslee of Washington State ordered on Monday that travelers from Britain and South Africa undergo a 14-day quarantine. He said more countries may be added to the travel proclamation.

Mr. Inslee said he was hopeful that the rules would help limit the spread of the mutation and said acting quickly was needed to make the effort successful. Mr. Inslee said the virus mutation was a warning that the nation is perhaps months away from the worst of the pandemic being over. “It is a vivid reminder of the uncertainties and unpredictability of this pandemic,” Mr. Inslee said.