Should I be concerned about the safety of the vaccine in Britain?
Britain’s drug regulator is seen as a bellwether agency, and its decisions often have influence abroad. In the case of the Pfizer vaccine, the agency has said that it did not cut any corners, and undertook the same laborious process of vetting the quality, efficacy and manufacturing protocols of the vaccine — except faster than usual.
Dr. Anthony S. Fauci, the United States’s top infectious disease expert, said last week that the British had not reviewed the vaccine “as carefully” as the United States was. But he walked back those comments the next day, saying: “I have a great deal of confidence in what the U.K. does, both scientifically and from a regulator standpoint.”

U.K. Covid Vaccine_ Side Effects, Safety, and Who Gets It First – The New York Times