Equalities minister Kemi Badenoch has spoken out against the abuse a university professor has faced for her views on gender identity.

Kathleen Stock, a professor of philosophy at the University of Sussex, has faced calls to be sacked amid accusations of transphobia.

But earlier this month, the University of Sussex vice-chancellor said the institution would not tolerate threats to “academic freedoms” after the campaign to remove Prof Stock from her position.

Last week, Prof Stock said she will be leaving her job after “an absolutely horrible time” and “a very difficult few years”.

Ms Badenoch told the Sky News’ Trevor Phillips On Sunday programme she is “appalled” at the way the professor has been treated, adding: “I went to Sussex University and I tweeted when I saw the university statement backing her, nobody should face bullying or harassment in the workplace. That is actually another thing that the Equality Act looks at, bullying and harassment.

“I don’t think she should lose her job. I think that she has every right to hold the beliefs… I think she is probably in step with the majority of the population.

“What we in Government are trying to do is show that we do believe that trans people should be free to live their lives as they wish, but where people see a conflict, and that conflict has tended to be around single-sex spaces and the definition of gender reassignment and how gender critical feminists, as they are known, believe that those rights are in conflict, what we can do in order to provide clarity.”

Announcing her departure on Twitter on Thursday, Prof Stock said: “This has been a very difficult few years, but the leadership’s approach more recently has been admirable and decent. I hope that other institutions in similar situations can learn from this.

“Am particularly glad to see University emphasising that bullying and harassment anyone for their legally held beliefs is unacceptable in their workplace.”

Ms Badenoch also insisted that while the Government does not believe in gender self-identification for trans people, there should be a process to get gender recognition certificates.

She said: “The Government position is that we will do everything we can to support trans people in particular, all LGBT people, but trans people in particular when it comes to healthcare, because they have different healthcare needs from other LGBT people.

“However, we do not think that goes as far as self ID, we do believe that there should be a process to get a gender recognition certificate, and the process does mean involving medical professionals as well.”

When told some trans activists would say the fact she does not accept the statement trans women are women is in itself a form of violence, Ms Badenoch said it is “sad that the debate has turned into one of name-calling”.

She added: “What I would ask people to do is actually look at what the policies are, what it is we’re doing in order to protect people of all types, whether they are LGBT, of different race, racial backgrounds, the different sexes.

“We are a Government that believes in equality and fairness for all, and everything we’re doing is to make sure that we have an equal society, and we should not get to a point where having a different opinion becomes a reason to insult other people. That’s absolutely wrong.”