LONDON — Islamic State propaganda had been found in the bag of one attacker while he was trying to board a flight in Italy. An F.B.I. informant said he had raised alarms about the second attacker two years ago. The third attacker, denied asylum in Britain, appeared to have sneaked in from Ireland.

The warning signs about the three assailants in a white van who smashed and stabbed their way through a trendy London neighborhood tumbled into the open on Tuesday, compounding the pressure on the police and Prime Minister Theresa May to explain them.

What has become clear since the Saturday night assault is that again and again, the young men who killed seven people before they were shot to death by the police had been reported to law enforcement authorities, bumping into what should have been the country’s security net, only for those signals to be played down, ignored or missed.

The latest revelations have placed Mrs. May, a former home secretary who was in charge of counterterrorism for six years before taking over as prime minister last year, under intense scrutiny two days before a general election. Even her own foreign secretary, Boris Johnson, a former London mayor, voiced the question many here are asking.