BEIRUT — The Islamic State group claimed responsibility Thursday for an attack by a man who plowed an SUV into pedestrians on a crowded London bridge and then stabbed a police officer to death on the grounds of Britain’s Parliament.

The attacker was born in Britain and known to authorities who had once investigated him for links to religious extremism, British Prime Minister Theresa May said Thursday in a sweeping speech in which she also encouraged Britons to go about their lives.