The Daily Mail reported that Quilliam has claimed of having evidence of the president of City University's Islamic Society, (ISoc) openly preaching extremism during prayers held inside the campus during the 2009-10 academic year in London.
They said the president, Saleh Patel, was recorded saying: "When they say to us the Islamic state teaches to cut the hand of the thief', yes it does! And it also teaches us to stone the adulterer."
"When they tell us that the Islamic state tells us and teaches us to kill the apostate, yes it does! Because this is what Allah and his messenger have taught us and this is the religion of Allah and it is Allah who legislates and only Allah has the right to legislate," he added.
The think tank reportedly interviewed students who claimed that the actions of leading members of the ISoc made members of the Lesbian, Gay, Bisexual and Transgender Society (LGBT) feel 'scared'.
Some Muslim students published an open letter complaining that their religion had been 'hijacked' by the ISoc.
Meanwhile, City University London Students' Union has released a statement which read: "The report raises a number of issues so the Students' Union will be in contact with the authors to review the evidence on which the report is based."