Zaghba, a 22-year-old with dual Moroccan-Italian nationality, was briefly detained after being stopped at the airport in Bologna, central Italy in March 2016.
Italian prosecutors were unable to bring charges against him for links to international terrorism and he was set free, a police spokesman told AFP.
Italy notified Britain and Morocco of his status as a potential Islamist radical.
But he never showed up on Britain’s radar as someone capable of involvement in an attack like Saturday’s, in which seven people were killed.
The three attackers smashed a van into pedestrians on London Bridge before going on a stabbing spree which ended with them being shot dead by police.
London’s Metropolitan Police said Zaghba had not been on their radar before Saturday, despite the Italian warning. He was not a “police or (intelligence agency) MI5 subject of interest,” a spokesman said.
The mayor of Valsamoggia, a municipality near Bologna, said Zaghba was the son of an Italian mother, Valeria Collina, and a Moroccan father, Mohamed Zaghba, who had separated 18 months ago.
The son had been registered at an address in the village of Castello di Serravalle since 2004, as an Italian living overseas.
“In fact he never lived here,” said the mayor, Daniele Ruscigno. “Only the mother lived here. She’d converted to Islam when she got married and neighbours say she wore a veil.”
Neighbours told AFP the mother had moved back to the village, one of five that make up Valsamoggia, 18 months ago, living on the ground floor of a two-storey house in a leafy setting.
PTI