Extremist groups should not be banned from speaking at British universities because students need to think about challenging "objectionable" ideas, Oxford University's new vice chancellor has said.

Professor Louise Richardson, the first woman to hold the role in the university's history, was installed in a ceremony at the Sheldonian Theatre on Tuesday.

She told The Daily Telegraph: "We need to expose our students to ideas that make them uncomfortable so that they can think about why it is that they feel uncomfortable and what it is about those ideas that they object to.

"And then to have the practice of framing a response and using reason to counter these objectionable ideas and to try to change the other person's mind and to be open to having their own minds changed."

Prof Richardson said provided organisations such as controversial human rights group Cage "can be countered, I think that we should let them be heard".

Prof Richardson, who is seen as a modernising figure, also labelled the all-male Bullingdon Club, which boasts Prime Minister David Cameron among its former members, as "completely unacceptable".

She told the Financial Times there was no formal link between Oxford and the Bullingdon Club but stressed: "If it had I would sever it or I would do my best to sever it."

She said that regardless of gender "anybody who goes out and smashes up any restaurant, I would think it's completely unacceptable".