British police say the two men identified are 27 year-old Khuram Butt and 30 year-old Rachid Redouane.
Khuram Butt was previously known to police and domestic spy agency MI5 and was a British citizen who had been born in Pakistan.
British police and security services had previously investigated one of the militants who carried out Saturday's attack in London, but due to limited resources he was not deemed enough of a threat to warrant close monitoring.
The vice-chair of the Police Federation for England and Wales, Calum Macleod, says the latest attack highlights a need for more resources.
"Since 2010 we have obviously been under a period of sustained cuts to policing budgets. We have lost 21,500 officers in that time. That has had an impact in relation to service delivery, an impact in relation to the safety of the public. We have also seen a reduction of about 1,200 firearms officers in that time. That is important, especially when you look across Europe, if you look within what is happening on our own shores at this time. We need the capability to defend the public, protect the public and preserve law and order."
The news increases pressure on Prime Minister Theresa May, who days before a national election is facing criticism for overseeing cuts to police during her years as interior minister.
On the campaign trail the Prime Minister did not respond directly to questions about funding cuts to police budgets.
Instead she urged voters to choose the Conservative party, saying the fight against extremism is an election priority.
"And it's also about, of course, ensuring we protect our national security and our defence, that we deal with the terrorists, we defeat the terrorists, but we also stand up to extremism that tries to divide our societies."
Meanwhile there are fears for a young Brisbane woman who was last seen on London Bridge before the attacks.
Family and friends of 21 year-old Sara Zelenak have taken to social media to appeal for information about the missing Australian who hasn't been heard from since the attacks.
Ms Zelenak is one of two people for whom Australian authorities are concerned.
Her mother, Julie Wallace, has told 97.3 FM in Queensland she's desperate for news about her daughter, who failed to return home after a night out when the attack happened.
"She left in March to explore the world. to go to Europe, she was with a host family looking after two little boys. The host rang to say they had given her the night off so she could go out with her friend and she was heading for the London Bridge where everyone goes on a Saturday night and all the action is - and she never came back."
More than 130 imams and religious leaders have refused to perform Islamic funeral prayers for the men who carried out the attack in London.
In a joint statement they said they had made the decision because the attackers' actions were indefensible and against the teachings of Islam.
London's Mayor, Sadiq Khan, led a vigil in London for the victims of the attack.
"I'm furious. These terrorists deliberately targeted innocent Londoners and visitors enjoying a night out on a Saturday night. They're justifying this horrific cowardly attack with a perverse, twisted, poisonous - what they would call - version of Islam. And I'm not having it. This is the month of Ramadan. I'm like many many Muslims, we're fasting, praying, giving to charity. And for these terrorists, for these extremists to try and justify their actions, using a twisted, perverted, poisonous form of Islam, I condemn them unequivocally."
