Read the statement in full made on Sunday morning.
Last night, our country fell victim to a brutal terrorist attack once again.
As a result I have just chaired a meeting of the Government's emergency committee, and I want to update you with the latest information about the attack.
Shortly before 10-past-10 yesterday evening, the Metropolitan Police received reports that a white van had struck pedestrians on London Bridge.
It continued to drive from London Bridge to Borough Market, where three terrorists left the van and attacked innocent and unarmed civilians with blades and knives.
All three were wearing what appeared to be explosive vests, but the police have established that this clothing was fake and worn only to spread panic and fear.
As so often in such serious situations, the police responded with great courage and great speed. 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.
The terrorists were confronted and shot by armed officers within eight minutes of the police receiving the first emergency call.
Seven people have died as a result of the attack, in addition to the three suspects shot dead by the police. Forty-eight people are being treated in several hospitals across London.
Many have life-threatening conditions.
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.
This is, as we all know, the third terrorist attack Britain has experienced in the last three months. In March a similar attack took place just around the corner on Westminster Bridge.
Two weeks ago the Manchester Arena was attacked by a suicide bomber and now London has been struck once more.
And at the same time the security and intelligence agencies and police have disrupted five credible plots since the Westminster attack in March.
In terms of their planning and execution, the recent attacks are not connected but we believe we are experiencing a new trend in the threat we face.
As terrorism breeds terrorism, perpetrators are inspired to attack not only on the basis of carefully constructed plots after years of planning and training, and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack.
We cannot and must not pretend that things can continue as they are. Things need to change and they need to change in four important ways.
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.
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.
Defeating this ideology is one of the great challenges of our time, but it cannot be defeated by military intervention alone.
It will not be defeated by the maintenance of a permanent defensive counter-terrorism operation, however skillful its leaders and practitioners.
It will only be defeated when we turn people's minds away from this violence and make them understand that our values – pluralistic British values – are superior to anything offered by the preachers and supporters of hate.
Second, we cannot allow this ideology the safe space it needs to breed.
Yet that is precisely what the internet, and the big companies that provide internet-based services, provide.
We need to work with allied democratic governments to reach international agreements that regulate cyberspace to prevent the spread of extremist and terrorism planning.
And we need to do everything we can at home to reduce the risks of extremism online.
Third, while we need to deprive the extremists of their safe spaces online, we must not forget about the safe spaces that continue to exist in the real world.
Yes, that means taking military action to destroy Isis in Iraq and Syria. But it also means taking action here at home.
While we have made significant progress in recent years, there is – to be frank – far too much tolerance of extremism in our country.
So we need to become far more robust in identifying it and stamping it out across the public sector and across society.
That will require some difficult, and often embarrassing, conversations.
But the whole of our country needs to come together to take on this extremism, and we need to live our lives not in a series of separated, segregated communities, but as one truly United Kingdom.
Fourth, we have a robust counter-terrorism strategy, that has proved successful over many years.
But as the nature of the threat we face becomes more complex, more fragmented, more hidden – especially online – the strategy needs to keep up.
So in light of what we are learning about the changing threat, we need to review Britain's counter-terrorism strategy to make sure the police and security services have all the powers they need.
And if we need to increase the length of custodial sentences for terrorist-related offences – even apparently less serious offences – that is what we will do.
Since the emergence of the threat from Islamist-inspired terrorism, our country has made significant progress in disrupting plots and protecting the public.
But it is time to say: 'Enough is enough.'
Everybody needs to go about their lives as they normally would. Our society should continue to function in accordance with our values.
But when it comes to taking on extremism and terrorism, things need to change.
As a mark of respect, two political parties have suspended our national campaigns for today. But violence can never be allowed to disrupt the democratic process, so those campaigns will resume in full tomorrow and the General Election will go ahead as planned on Thursday.
As a country, our response must be as it has always been when we have been confronted by violence.
We must come together, we must pull together, and united we will take on and defeat our enemies.