Professor Mary Beard describes herself as having a thick skin. But over the past 10 days, during which the 58-year-old classicist has been subjected to a stream of vitriolic online abuse after an appearance on Question Time, even she has struggled to keep on an even emotional keel.

"I only had a little weep once, though," she admits. "That was when a colleague sent a really nice tweet. It just opened me!"

In fact, she says, her colleagues and students have been hugely supportive. "One very senior colleague in college emailed to say how proud she was of me. In the eyes of some, I'm still young. It's hugely reassuring!"

It all started when Beard appeared as a panellist on the BBC1 programme, filmed in Lincoln. In response to a question about whether the UK could cope with more immigration, she cited a recent report claiming that immigration had actually brought some benefits to the local area. A perfectly reasonable thing to say, or so you might have thought.

But the next day, commenters on the now closed Don't Start Me Off website, which encouraged anonymous posters to vent their anger on targets chosen by the administrator, launched a vicious and sustained attack on Beard. The internet trolls posted dozens of horrifying sexual taunts, in language too offensive to reprint. The level of the abuse was so shocking that even those accustomed to the cut-and-thrust of online debate were appalled.

In one of the milder examples, Beard was called "a vile, spiteful excuse for a woman, who eats too much cabbage and has cheese straws for teeth". Beard's features were even superimposed on an image of female genitalia.

"It was so ghastly it didn't feel personal, or personally critical," Beard says now, with the benefit of considered hindsight. "It was such generic, violent misogyny. In a way, I didn't feel it was about me."

The controversy led to the website being shut down by its administrator last Tuesday. But the experience has had a lasting impact on Beard, who says it left her feeling "a sense of assault". She reeled from it as though from "a punch".

Is the level of vitriol she faced indicative of the fact that some men – and it is, by and large, men – simply do not like the idea of an unapologetically clever woman who doesn't use Botox or hair dye voicing her opinions on screen? Is the idea that she refuses to conform somehow disturbing to them?

"One issue must be, as you say, that actually a woman, 58 and looking it, saying what she thinks, against the grain, is explosive," Beard says. "But that can't quite be all. There's real frustration coming out in those vile comments. Sure, it's misogyny, but it is also alienation and resentment, understandably, about the voice and the right to speak.

"The web is democratising and also the voice of people who don't think they have another outlet. And that voice can be punitive."

Beard is just the latest in a dispiritingly long line of high-profile women who have been subjected to online threats and harassment. They include former Conservative MP Louise Mensch (whose children were threatened by a Twitter user) comedian Shappi Khorsandi and the celebrity chef Lorraine Pascale.

On her own blog, A Don's Life, Beard wrote that the abuse showed classic signs of vile playground bullying: "It would be quite enough to put many women off appearing in public, contributing to political debate."

Beard, one of the country's foremost classicists, has never been particularly interested in her appearance, preferring to concentrate on what she thinks and how best to communicate it. Her long hair is left unashamedly grey and her face bears the marks of her life.

And this, in itself, is a form of attractiveness. For many women, she is something of a hero: a refreshing presence in a television industry dominated by endless youth and cookie-cutter beauty.

But this means she is no stranger to name-calling. When Beard presented the BBC2 series Meet the Romans last year, the television critic AA Gill wrote that she should be "kept away from the cameras altogether" and was "this far from being the subject of a Channel 4 dating documentary" (thought to be a reference to The Undateables, a controversial series on that channel about people with disabilities trying to find love).

Beard remains sanguine. "Grey is obviously something most women on TV don't do," she says. "But I think most people tuned into Meet the Romans because they wanted to learn about the Romans. And what I had to say was important. Grey is my hair colour. I really can't see why I should change it. There clearly is a view of female normative beauty but more women of 58 do look like me than like Victoria Beckham."

After the Question Time debacle, male commentators once again waded in. The Spectator columnist Rod Liddle wrote that most of the blog comments were simply: "accurate refutations of her vacuous argument" on the benefits of immigration.

He then revealed that he was running a competition to find "the most stupid woman" to have appeared on Question Time over the last 12 months.

Why does Beard think she provokes such ire?

"I really don't know," Beard says. "I guess it is something to do with the combination of the charged issue of migration and the charged issue of misogyny. Together [they're] explosive.

"But I would like to draw a distinction between Gill and these guys. I'm not defending Gill, and there is a sense of continuity between various forms of misogyny, but Gill was not commenting anonymously, and it really didn't have the sexual violence of the Don't Start Me Off site in any way."

Liddle was another matter. "I was just gobsmacked," she says. "This was the site that had talked about dicks down my mouth and had published the picture of me plus labia superimposed … I thought Liddle was playing up to some bloke-ish image. It's interesting that he didn't have a competition for 'worst man' on Question Time."

Some of her tormentors have since apologised. "It has been touching," Beard says. "It is always hard to apologise and I am grateful to the many that have done so."

The closure of the site is, she thinks, "a braver decision than simply hanging on – credit to them for that".

And there has been a lot of support, too. "Over the past few days, people have come up to me on the train and said 'Don't let them get you down'. I've had more supportive tweets and emails than ever – from friends, strangers and colleagues – making the point that it was really important to do this for the young women. I've had tweets about people at school doing it in their Latin classes."

In the midst of the furore, Beard has returned to work – marking essays, taking tutorials and getting to grips with the finer points of Plato. Her husband Professor Robin Cormack, a classicist and art historian, has been "wonderfully tolerant. He helps a lot in keeping a sense of proportion. He has no truck with the silliness."

She has also discussed the politics of what happened with her students. So, are there instances of women being harangued for the same reasons in classical antiquity?

"Classical antiquity is always much more complicated than you think. But the basic position is that elderly men are admirable and elderly women are awful [because] what is the point of a post-menopausal woman? Old women get laughed at. I thought we had moved on."

Beard doesn't want the internet to be policed. She knows that unacceptable things will always be posted. "We are still working out the boundaries. The key is [that] we learn to say 'Hey – that's not on,' and to say sorry."

Will she ever appear on Question Time again?

"Sure," she says. "This hasn't been easy. But you let every other woman down if you don't."