One of the attackers is believed to have lived in Ireland for a short time
Counter-terror agencies are under the spotlight after it emerged one of the London attackers was known to security services.
Khuram Shazad Butt was investigated in 2015, but officers insisted there was no evidence to suggest an attack was being planned.
He was therefore "prioritised in the lower echelons of our investigative work," police said.
Metropolitan Police Assistant Commissioner Mark Rowley defended the actions of the security services.
"At any one time MI5 and police are conducting around 500 active investigations, involving 3,000 subjects of interest.
"Additionally, there are around 20,000 individuals who are former subjects of interest, whose risk remains subject to review by MI5 and its partners."
Scotland Yard has named two of the terrorists involved in the London Bridge attack as Khuram Shazad Butt and Rachid Redouane.
Butt was known to police and MI5 and Assistant Commissioner Mark Rowley said an investigation into him started in 2015. But with "no intelligence to suggest that this attack was being planned...the investigation had been prioritised accordingly".
Butt appeared in a Channel 4 documentary called The Jihadis Next Door last year.
He was once asked to leave a mosque in east London after "interrupting a Friday sermon".
In his neighbourhood, Butt was known as Abu Zaitun - or Abu for short.
The 27-year-old came to Britain as a child when his parents sought asylum from Pakistan - and he lived in a ground-floor flat in Barking.
Neighbours said he was a keen gym-goer and weightlifter, and was the father of a baby and a toddler.
An online CV shows that Butt obtained an NVQ in business administration in 2009, and a diploma in teaching English to adults in August 2016.
The CV lists two jobs: one he started in May at Transport for London, and another at a company called Auriga Holdings, which we believe to be a franchise for a local KFC restaurant.
Redouane was 30 years old and born in July 1986. He claimed to be Moroccan and Libyan.
Scotland Yard says he also used the name Rachid Elkhdar, as well as a different date of birth which made him five years younger.
Redouane was not known to those authorities.
It's reported that an Irish ID card was found on Redouane's body. Reports have said he lived in Rathmines, Dublin. It is believed he used Irish jurisdiction to get a European Union permit allowing him to be in the UK.
Police in Ireland are investigating, with detectives trying to establish whether he travelled to Syria.
He is understood to have lived in the Rathmines area of Dublin for 18 months between 2014 and 2016. He was married to a Scottish wife.
The third London attacker has been named by British police as a Moroccan-Italian man, Youssef Zaghba.
He was not a subject of interest to either UK officers or MI5.
Italian newspaper Corriere Della Sera reported that he was born in Fez in January 1995 to a Moroccan father and an Italian mother.
The paper said his parents had lived in Morocco before splitting up.
His mother apparently then returned to Italy and lived in the Bologna area.
He was reportedly stopped at Bologna airport in March last year while trying to take a flight to Istanbul, before potentially travelling on to Syria.
He is said to have had one backpack with him, and a one-way ticket.
Zaghba apparently told his mother he was headed for Rome.
It is reported that there were pictures and videos on his phone on religious themes, but nothing of particular significance in relation to jihadist ideology.
Meanwhile, police confirmed that 12 people arrested on Sunday in connection with the attack have now been released without charge. They had detained seven men and five women and have also searched six properties as part of their investigation.
Of the 48 people taken to hospital with injuries from the attack, 36 are still receiving treatment, with 18 of those in a critical condition.
Police are still working to advise the families of those killed, something which is taking longer than usual as some are from overseas.
The second victim to be named is James McMullan, 32, from Hackney, His sister Melissa McMullan described him as an "inspiration" and a "unique personality".
Canadian Christine Archibald, 30, died after being struck by the attackers' speeding van on London Bridge.
A French national has also been confirmed as having been killed but this person has not yet been publicly named.
Among those still missing are a Spanish national and an Australian.
Additional reporting from IRN