Groups representing students and universities have expressed caution at plans for a "free speech champion" to regulate England's campuses.
The government has announced plans for the role to ensure freedom of speech and expression is not stifled.
The National Union of Students says there is "no evidence" of a freedom of speech crisis on campus.
And the Russell Group of leading universities says universities need to keep their "institutional autonomy".
The group warned against creating an "unnecessary and burdensome bureaucracy".
The new post - which will have a seat on the Office for Students' (OfS) board - is part of a series of proposals, announced on Tuesday, aimed at strengthening academic freedom in England's universities.
Under the plans, universities would be legally required to actively promote free speech and the OfS would have the power to impose fines on institutions if they breach this condition.
This would also extend to student unions, which would have to ensure that lawful free speech is secured for members and visiting speakers.
Individuals would be able to seek compensation through the courts if they suffered loss from a breach of the free speech duties - like being expelled, dismissed or demoted - under a new legal measure.
The Department for Education said the next steps for legislation would be set out "in due course".
Education Secretary Gavin Williamson warned of the "chilling effect" of "silencing" in universities.
Mr Williamson said: "Free speech underpins our democratic society and our universities have a long and proud history of being places where students and academics can express themselves freely, challenge views and cultivate an open mind.
"But I am deeply worried about the chilling effect on campuses of unacceptable silencing and censoring.
"That is why we must strengthen free speech in higher education, by bolstering the existing legal duties and ensuring strong, robust action is taken if these are breached."
A mix of opinion
Catherine, a student at the University of Central Lancashire, told the BBC: "I don't think it's silencing to say 'this view isn't acceptable' or to refuse to give them a platform.
"Freedom of speech doesn't mean you have freedom from consequences - I think a lot of people confuse free speech as meaning that they can say whatever they want and nothing will happen to them."
Catherine said the government's proposal of a free speech champion could be problematic.
"I think this new role from the government is a good idea in principle, but in reality it has the potential to go wrong because different views can mean a lot of things and it could result in people not being respectful to one another."
But Paul from Gloucestershire said there was a problem with freedom of speech on university campuses, with students having to have the "right opinion".
"My son was treated dreadfully at university because of his beliefs and opinions.
"He was shunned, ostracised and even threatened with violence simply because he voted for Brexit and held conservative views.
"If you don't have an opinion which is mainstream, for want of a better word, there are labels for you."
Paul said his son had been looking forward to having good debate at university with people who held different opinions, but was "very disappointed".
"In my experience, university life can be miserable if you don't hold Marxist, communist or socialist views."
The Russell Group responded cautiously to the government's proposal.
"It is important that proposals in this government policy paper, if taken forward, are evidence-based and proportionate, with due care taken to ensure academic freedom and institutional autonomy.
"Government should support existing work by universities and students' unions to defend and maintain freedom of expression on campus, rather than adding unnecessary and burdensome bureaucracy."
Hillary Gyebi-Ababio, the National Union of Students vice-president for higher education, said: "Students' unions are committed to freedom of expression and are the very home of rigorous debate and new ideas.
"There is no evidence of a freedom of expression crisis on campus, and students' unions are constantly taking positive steps to help facilitate the thousands of events that take place each year."
Jo Grady, general secretary of the University and College Union, which represents staff, said: "In reality the biggest threats to academic freedom and free speech come not from staff and students, nor from so-called 'cancel culture', but from ministers' own attempts to police what can and cannot be said on campus."
A failure to "get to grips with the endemic job insecurity and managerialist approaches which mean academics are less able to speak truth to power" were also a barrier to free speech, said Ms Grady.
Peter Tatchell, a gay rights activist, said the plan for a free speech tsar was part of a "cynical culture war" to use "hot-button culture issues" to secure political advantage.
Mr Tatchell, who has himself been the target of no-platform protests, told BBC Radio 4's Today programme that said such issues were "quite rare" and needed to be put in perspective.
Prof Selina Todd, an Oxford University academic who previously had an invitation to a conference celebrating women withdrawn over her stance on transgender rights issues, welcomed government action although she said the free speech champion could be a "blunt instrument".
She told BBC Radio 4's Today programme that universities have "dismally failed" to uphold freedom of debate in recent years.
"Things have got a lot worse for academics and for students - many of whom get in touch with me anonymously to say how frightened they are to speak out," she said.
In December, Cambridge University said its proposed statement on free speech would no longer require staff and students to be "respectful" of differing views, following an intervention from academics who said calling for respect could undermine academic freedom.