LONDON—The U.K. grew to become the initially Western country to grant crisis-use authorization for a Covid-19 vaccine, clearing a shot created by Pfizer Inc. of the U.S. and BioNTech SE of Germany to be dispersed in constrained numbers within just days.

The two-shot vaccine is also currently being reviewed by the Food and Drug Administration in the U.S., in which a similar authorization could occur afterwards this month and a rollout in advance of the finish of the year.

The…