Facebook and Twitter have been accused of allowing Islamophobia to flourish by refusing to remove hundreds of inflammatory posts which have been reported by anti-racism campaigners.

Some of the posts which have been flagged up to the two social media sites include accusations of Muslims being rapists, paedophiles and comparable to cancer.

In one shocking example, a Facebook user, who was referring to the beheading of Westerners in Syria said: 'For every person beheaded by these sick savages we should drag 10 off the streets and behead them, film it and put it online.

Facebook has been accused of allowing Islamophobia to flourish by refusing to take down hundreds of inflammatory posts from their sites. Pictured: CEO Mark Zuckerberg speaking in California in 2013

'For every child they cut in half … we cut one of their children in half. An eye for an eye.'

But, in several cases, the accounts behind the abusive messages have not been suspended, nor have the posts been removed, according to a report by The Independent.

Facebook said it had to 'strike the right balance' between freedom of expression and maintaining 'a safe and trusted environment', while Twitter maintained that all reports against the site's rules were investigated.

The investigation also found that the volume of posts have increased significantly in the wake of the Rotherham sex abuse scandal and the beheading of British hostages by ISIS fanatics.

Over the past four months, Muslim groups have been compiling details of online abuse and reporting it to Twitter and Facebook.

They have reportedly brought hundreds of messages to the attention of the social-media companies, but the accounts are still easily accessible.

One prolific tweeter, who has been reported several times, wrote on New Year's Eve: 'Should have lost World War Two. Your daughters would be getting impregnated by handsome blond Germans instead of Pakistani goat herders. Good job Britain.'

One man, Eric King, who was branded a 'vile, reprehensible bigot' after he sent offensive photographs and social media posts to an Islamic community centre near Truro, was given a suspended sentence for his crime.

Twitter said it investigates all abuse reported against its rules, but anti-racism groups say they have found several tweets which are inflammatory and have not been taken down

But his Facebook account, which he used to send abusive messages to the same mosque and is still using to convey his message, is still active.

Fiyaz Mughal, director of Faith Matters, an interfaith organisation which runs a helpline called Tell MAMA, for victims of anti-Muslim violence, said he was disappointed the sites were not taking a stronger stance.

It is morally unacceptable that social media platforms... leave up inflammatory, highly socially divisive and openly bigoted views Fiyaz Mughal, director of Faith Matters

He said: 'It is morally unacceptable that social media platforms like Facebook and Twitter, which are vast profit-making companies, socially engineer what is right and wrong to say in our society when they leave up inflammatory, highly socially divisive and openly bigoted views.'

Mr Mughal said that Tell MAMA regularly receives reports of anti-Muslim rhetoric and hate from concerned Facebook and Twitter users.

In October, the Metropolitan Police also released figures to show hate crime against Muslims in London had risen by 65 per cent over the previous 12 months.

Latest figures also suggest that anti-Muslim hate crime has risen sharply following the murder of Lee Rigby in 2013.

In a statement Facebook said it had a clear policy for deciding what was and what was not acceptable freedom of speech. 'We take hate speech seriously and remove any content reported to us that directly attacks others based on their race, ethnicity, national origin, religion, sex, gender, sexual orientation, disability or medical condition.

The volume of posts have increased significantly in the past few months, in the aftermath of the Rotherham sex abuse scandal and the murder of British hostages held by ISIS. Pictured: The ISIS flag

'With a diverse global community of more than a billion people, we occasionally see people post content which, whilst not against our rules, some people may find offensive.

'By working with community groups like Faith Matters, we aim to show people the power of counter speech and, in doing so, strike the right balance between giving people the freedom to express themselves and maintaining a safe and trusted environment.'