One of the London Bridge attackers appeared in a TV documentary called The Jihadis Next Door.
Khuram Shazad Butt, known to friends and neighbours as "Abz" was filmed by Channel 4 for the programme.
At one point the 27-year-old was seen among a group of British jihadis praying with a black Islamist flag in London's Regent's Park.
He was shot and killed by police after he and two others attacked people on London Bridge with a van and knives, police said.
His neighbours were not aware he had appeared in the programme. Some described him a "family man" who they believed had a string of short-term jobs, working for Transport for London and KFC among others.
Naming Butt and an accomplice, police admitted he was known to them and MI5, but that "there was no intelligence to suggest that this attack was being planned and the investigation had been prioritised accordingly".
His accomplice, Rachid Redouane, 30, was not known to authorities. Both men were from Barking in east London.
The Metropolitan Police said: "Khuram Shazad Butt was known to the police and MI5. However, there was no intelligence to suggest that this attack was being planned and the investigation had been prioritised accordingly. The other named man, Rachid Redouane, was not known."
The force added: "Work is ongoing to understand more about them, their connections and whether they were assisted or supported by anyone else."
Detectives were "particularly keen to hear about places they may have frequented and their movements in the days and hours before the attack," it said, adding: "The investigation into this horrific attack is fast-moving and complex as we piece together a fuller picture of what occurred."
Officers have arrested 12 people — seven women and five men — and searched six properties. One of the arrested men and one of the women were subsequently released."
The UK is facing a "severe and high tempo terrorist threat", the force said.
