Some of the missed warnings were especially glaring because they came from the very people the British government had entrusted with identifying extremists.

Usama Hasan, a former Islamic extremist who now works with the police to help de-radicalize others, said he had a physical altercation in a London park less than a year ago with one of the assailants, Khuram Shazad Butt.

Mr. Butt’s brother, Saad, who did paid work for the police on counterextremism issues and was estranged from the assailant, missed signs of how dangerous his brother’s extremism had become.

Other warnings had also been raised about Mr. Butt, 27, who held odd jobs, including at KFC and a six-month stint as a customer service trainee for the London subway system that ended in October. His second child was born weeks before the attack, neighbors said.