A strict ban was placed on the use of visual or audio recording equipment of Assange's appearance at the university, while journalists were also barred from attending.
Around 800 people were understood to have turned up to see Assange speak, with a queue for entry stretching more than 40 metres long.
In a report published by Varsity, the student newspaper for the University of Cambridge, it was alleged that two members of the audience were "escorted off the premises during the talk for allegedly using recording equipment".
According to Varsity one of the students was later apologised to after he claimed he was using his mobile phone to text.
Speaking exclusively to members of the union and overseen by a team of eight security guards, Assange said that while the ban was "a bit rough" it helped to avoid a "press conference", Varsity's report adds.
Speaking to another student title before the event, The Tab, president of the union society Lauren Davidson insisted that a press ban "is the norm".
"A lack of press presence is our default position, as opposed to the other way round," she is quoted as saying.
During his speech Assange was said to have discussed a range of topics including the US diplomatic cables, the privatisation of censorship, the role of the internet and the uprisings in the Middle East.
Image by Bill Bailey.