The new head of the University of Oxford has spoken out in support of extremist groups being allowed to speak on campus.

Professor Louise Richardson, an Irish political scientist who specialises in terrorism and who was formerly at the University of St Andrew's in Scotland, said students need to be allowed to hear extremist views to help them think about how to challenge "objectionable" ideas.

Richardson, who is the first woman to be vice-chancellor at Oxford, said in an interview with 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."

Freedom of speech campaigners are growing increasingly concerned about restrictions placed on extremists at some universitites. Oxford's student newspaper Cherwell surveyed students over the controversy about the Cecil Rhodes statue and the imperialist's colonial past. More than a third of students thought the statue should go. Among black and  minority ethnic students, the proportion was higher, at nearly half.

Speaking to the Daily Telegraph from her new offices in Oxford, Prof Richardson said: "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 about and what it is about those ideas that they object to."

They should then have the practice of framing a response and using reason to counter these objectionable ideas, to try to change the other person's mind and to be open to having their own minds changed. "That's quite the opposite of the tendency towards safe spaces and I hope that universities will continue to defend the imperative of allowing even objectionable ideas to be spoken."

In a separate interview with The Financial Times she also said elitist all-male clubs such as the Bullingdon, whose former members include Prime Minister David Cameron, Mayor of London Boris Johnson and Chancellor George Osborne, were "completely unacceptable".

She said Oxford had no formal link with the club. "If it had I would sever it or I would do my best to sever it."

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

Several universities are currently being investigated over allegations that they allowed meetings to be held on campus during which unopposed speakers for a group called Cage, an advocacy organisation that campaigns against the War on Terror, advised students how how they could avoid being deradicalised by the Government's anti-extremism strategy Prevent.