The universities minister has announced plans to prevent student organisations from silencing speakers in public debates.
Universities which fail to comply could be publicly censured and even fined as concern grows about being debates being closed down and speakers no-platformed.
Both Christ Church and the University of Kent have had issues with free speech in the recent past. Neither received wholly positive assessments in this year’s free speech rankings.
In 2015, a student union official from Kent said that the union itself would decide which views could be heard and which couldn’t, prompting critics to complain that it gave it the power to deny opinions which it merely opposed.
In the same year, National Union of Students LGBT officer Fran Cowling refused to take the stage at Christ Church with veteran gay rights campaigner Peter Tatchell because he had defended feminist Germaine Greer’s right to her opinion on transgender issues.
Announcing the crackdown on free speech restrictions, Mr Gymiah said: “It’s time to address this problem.
“The current landscape around free speech on campus is murky at best with a dizzying array of disjointed guidelines for universities, student unions and associations to follow.
“When there are so many different interpretations of the rules, there is the risk that legal free speech will be stifled, either by well-intentioned but jittery managers, or by ill-intentioned wreckers.
“University should be an assault on the senses, it should make you question your ideas and expose you to opinions you might not agree with.
“To have a frank discussion about free speech means we need to be honest and we need the courage to act.”
In February, the online magazine Spiked published its free speech rankings for UK universities for 2018.
It gave Christ Church a red mark because its union had “collectively created a hostile environment for free speech”. Kent received a yellow mark because it “chilled free speech through intervention”.
Mr Gyimah added: “I am hosting free speech summit, bringing together leaders from across the higher education sector, including Universities UK, the NUS, the equalities and human rights commission and the charity commission which regulates students’ unions.
“I’m calling on them to clarify the rules and regulations around speakers and events, to make sure they are not a barrier to free speech within the law.”