Facebook has removed a video of a woman being beheaded and updated its policy on graphic violence following a public outcry against the world’s largest social media website.

In a move which David Cameron described as “irresponsible”, Facebook said on Monday that it would be allowing users to upload images and videos of graphic violence so that they could be “condemned”.

It has now backtracked on that decision, moving to take down a particular video which sparked this week’s debate. Entitled only “Challenge: Anybody can watch this video?” and carrying no warning of graphic content, it seemed to show a masked man beheading a woman in Mexico.

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The operators of the site, which has 1.15 billion users and can be accessed from the age of 13, said yesterday that they have decided to “strengthen” Facebook’s policy on graphic violence.

That does not mean it will be reinstating a blanket ban on all decapitation videos – a temporary measure which was recently lifted.

In a statement, Facebook explained: “When we review content that is reported to us, we will take a more holistic look at the context surrounding a violent image or video.

“Second, we will consider whether the person posting the content is sharing it responsibly, such as accompanying the video or image with a warning and sharing it with an age-appropriate audience.

“Based on these enhanced standards, we have re-examined recent reports of graphic content and have concluded that this content improperly and irresponsibly glorifies violence. For this reason, we have removed it.”

The decision will be welcomed by those who condemned Facebook for allowing such videos to be posted in the first place, but does not bring an end to the question of how the site will police users’ reactions to violent images – or indeed if it should.

Such challenges are a mark of the site’s attempts to reposition itself in a current affairs market – seeking to compete with micro-blogging platforms like Twitter as a place where people discuss the most up to date and controversial matters of the day.

Facebook polices its site to remove pornography, hate speech and other forbidden content, and has a long-established system of tools which users can turn to if they want to report something to moderators – a level of responsibility which is relatively new to Twitter.