As many as 15,000 items of "jihadist propaganda" have been taken down from the internet due to government pressure since December 2013, Downing Street said on Monday.
David Cameron said the "extremist poisonous narrative" leading people to fight in Syria could end up with "people dead on our own streets".
His official spokeswoman revealed that the British government was pressing YouTube to take down a video posted three days ago by a Cardiff-born man now in Syria calling for fellow British Muslims to join the war in Syria.
She said the video should not be hosted by YouTube. Parts of the video have also been hosted by a number of news websites including Mail Online and the Telegraph.
Cameron said in a statement: "We are putting more of our resources in terms of intelligence, security [and] policing into stopping people to travel to Syria, monitoring them properly when they return and making sure we reduce the risk to our country. The most important thing of all is to stop this radicalisation in the first place.
"That's why my counter-extremism taskforce is about driving out the extremist, poisonous narrative and getting it out of our schools, getting it out of our universities, getting it out of our campuses, getting it out of our prisons, confronting it wherever it appears, because we know the end part of this extremist narrative can mean people dead on our own streets."
The scale of the government activity may reflect an increase in British government monitoring or alternatively an increase in the number of such videos being posted in the UK. Either way it represents a huge logistical problem for the government.
Nasser Muthana, a 20-year-old medical student, can be seen in the Syria video wearing a white turban and claiming that the Islamic State in Iraq and the Levant (Isis) has fighters from as far afield as Cambodia, Australia and the UK.
His family, from the Cardiff area, said he had travelled to join the conflict with his brother Aseel, 17. Their father, Ahmed Muthana, has said he is "heartbroken" that his sons left the UK to fight in Syria, and told the Guardian that they had "betrayed Great Britain".
A YouTube spokesman said: "YouTube has clear policies prohibiting violent content or content intended to incite violence, and we remove videos violating these policies when flagged by our users. We also terminate any account registered by a member of a designated foreign terrorist organisation and used in an official capacity to further its interests.
"We allow videos posted with a clear news or documentary purpose to remain on YouTube, applying warnings and age-restrictions as appropriate."
A Twitter spokesman said it did not actively monitor content on the platform but its rules "prohibit the publication or posting of direct, specific threats of violence against others or any unlawful use".