A High Court judge has rejected calls from the father of a troubled 13-year-old to force Facebook to forbid her from accessing her account in a case which highlights the difficulties some parents face in stopping children accessing inappropriate content online.

The father, who cannot be named for legal reasons, wanted judges to force Facebook to take “any steps necessary” in stopping the girl accessing the website after she used it to post a series of sexually suggestive pictures and have “sexualised contact” with older men.

However Facebook admitted that it was powerless to stop the girl using an account because she could simply create new ones under different pseudonyms and access the site from a multitude of different devices.

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The case illustrates some of the concerns parents have over lax controls and monitoring systems Facebook employs for the more than one billion users who have signed up to a profile with the social media giant. Although Facebook insists only those aged 13 or above can create a profile on their site, the social network does not use any age or identity verification systems. Instead it relies on users to report content that is inappropriate or breaches the site’s lengthy terms and conditions.

Sitting in the High Court in Belfast, Mr Justice McCloskey said Facebook’s defence largely rested on the idea that “it has created something of a monster which it alleges it cannot control”.

Nonetheless he threw out the father’s bid for an interim injunction forcing Facebook to halt the girl accessing the site because it was far too broad in its scope, was unworkable and could not be monitored.

The girl herself has a troubled background and a history of inappropriate, over-sexualised behaviour. She is described as a “vulnerable young lady who is beyond parental control” and who has spent much of the last two years in a secure unit. She has repeatedly absconded and been found in company of older males consuming drugs and alcohol.

Over the course of a nine month period in 2011 the girl – who was then aged 12 - created a total of four Facebook profiles in which she often posted explicit photos and had inappropriate contact with older men. Each time the girl’s father complained using Facebook’s reporting procedures and the profiles were taken down within 24 hours. In one profile, the girl had joined a group containing 63,000 members which encouraged users to send in sexually suggestive photographs.

Whilst in care the local authorities and her parents took steps to stop her accessing the internet via different devices and the judge found that there was no evidence any offending publication has exposed her to risk since the summer of 2012. However the girl has recently left secure accommodation to live with her mother. According to a statement provided by her father, she has claimed to have set up a new Facebook account under a false name which her parents cannot access or find.

In a defence submitted to the court, Facebook said there was little way it could monitor whether the girl went on to set up new profiles. “It would be unfeasible for Facebook to review over 1 billion profiles and millions of uploaded posts to determine if a particular individual has posted content online,” the website stated. “All Facebook can do is act expeditiously every time it receives a report about unlawful or abusive content.”

The site also insisted that much of the responsibility for how teenagers or children access the site should rest with the parents. “Facebook rejects the notion of broad censorship to prevent a single individual from creating a user account and profile,” the website’s defence stated. “At some point, responsibility must rest with a parent or guardian.”

However Mr Justice McCloskey predicted that Facebook’s argument that it was effectively powerless to stop certain children accessing the site might not be successful “in an appropriate case” in the future and would need to be probed in further legal action.

“It is inevitable that this plea of impotence will be subjected to intense judicial scrutiny, not least because the proceedings involve a child,” he said.