The Conservative leader, in a hard-hitting statement, vowed that Britain would "defeat our enemies" and that the country needed to be a "United Kingdom" against terrorism.
During an at times emotional and powerful address, the PM hit out at extremists for spouting a "perverse" ideology that did not reflect the truth.
Speaking outside Downing Street, Mrs May said: "We must come together, we must pull together, and united we will take on and defeat our enemies."
She added: "First, while the recent attacks are not connected by common networks, they are connected in one important sense. They are bound together by the single evil ideology of Islamist extremism that preaches hatred, sows division and promotes sectarianism.
Theresa May outside Downing Street earlier today Morning after London attack: Heightened police presence at Borough Market & Bridge Sun, June 4, 2017
SIX people have been killed after a horrific terror attack targeted London Bridge and Borough Market on Saturday night. These are the pictures are London wakes up to the tragic scenes
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"It is an ideology that claims our Western values of freedom, democracy and human rights are incompatible with the religion of Islam. It is an ideology that is a perversion of Islam and a perversion of the truth."
She also confirmed that the General Election would still go ahead as planned on Thursday.
In a statement outside Number 10, she paid tribute to the police and emergency services that were in attendance as well as members of the public.
Police and the emergency services attend the scene at London Bridge
She said that “thoughts were with the families affected”.
May also paid tribute to the response of the emergency services, saying: "As so often in such serious situations, the police responded with great courage and great speed.
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"Armed offices from the Metropolitan Police and the City of London Police arrived at Borough Market within moments and shot and killed the three suspects.
Theresa May addresses the nation outside Downing Street
"The terrorists were confronted and shot by armed officers within eight minutes of the police receiving the first emergency call."
She added: "On behalf of the people of London and on behalf of the whole country, I want to thank and pay tribute to the professionalism and bravery of the police and the emergency services, and the courage of members of the public who defended themselves and others from the attackers.
"And our thoughts and prayers are with the victims and with their friends, families and loved ones."
Armed police patrolled the London Bridge area
Speaking outside Downing Street, Mrs May said that although there was no direct link between the three incidents, "terrorism breeds terrorism" and that they all shared the same ideology of “evil Islamist extremism”, an ideology that was a “perversion of Islam and the truth”.
She added that the ideology had to be defeated.
She continued: "We are experiencing a new trend in the threat we face as terrorism breeds terrorism."
Setting out an outline for a plan of action, Mrs May said that there should be no "safe place" either online or the "real world" for the extremist ideology to flourish.
She also urged the need to have a review of counter-terrorism strategy.
Mrs May said" "It is time to say enough is enough […] Things need to change."