The abuse row that has engulfed Twitter shows no signs of abating – after the historian Mary Beard felt compelled to break a day-long boycott of the site to reveal the latest death threat.

On perhaps the darkest day yet for the social network, even Professor Beard’s disclosure provoked only more arguments, as the journalist Giles Coren publicly criticised her for failing to maintain solidarity with the social networking silent protest.

Professor Beard had tweeted on Saturday evening that she planned to be among those avoiding the website for the day, along with a number of public figures including the journalists Caitlin Moran and Suzanne Moore, the magician Derren Brown and the comedian Sarah Millican.

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The day-long boycott of the service was organised in protest against abusive tweets being sent to prominent women including the Labour MP Stella Creasy and the feminist campaigner Caroline Criado-Perez.

This morning, however, Professor Beard broke her silence, writing: “Planned to be off twitter, but I’ve had more threats this morning (rape and worse). It is still going on. Tried to report to Twitter, failed.”

She later posted: “Sexist abuse is one thing, threats of violent decapitation quite another,” adding that she had referred the messages to the police. Only hours earlier she had alerted police to a bomb threat she had received via Twitter.

Yet the journalist Giles Coren argued that Professor Beard was leaving herself open to being abused by ignoring her own pledge to stay off Twitter for the day.

“But isn’t the point that if you’re not looking it’s not there? If you weren’t on, you wouldn’t have seen them? Then they’d stop,” he wrote to her, adding: “In short, if a tree falls on Twitter, but you’re not on Twitter…”

As others defended Coren, however, he later remarked: “We are arriving at the point where the anti-trolls are becoming as frothed-up, mental, mob-happy and bloodthirsty as the trolls. Sad days.”

Professor Beard, 58, had told BBC Radio 5 Live: “There’s something very strangely and awkwardly insidious about it. It is scary and it has got to stop. I didn’t actually intellectually feel that I was in danger but I thought I was being harassed, and I thought I was being harassed in a particularly unpleasant way.”

As part of their investigation, police have arrested a 25-year-old man in the North-east and a 21-year-old man in the Manchester area over the threats to Ms Creasy and Ms Criado-Perez.

Tony Wang, the general manager of Twitter UK, apologised at the weekend to women who had experienced abuse on the site, saying it was “simply not acceptable”, and announced updated rules and a new button to report abuse aimed at tackling the problem.

The changes came as a petition calling for tighter regulation of Twitter had received 127,000 signatures.

Police are also investigating bomb threats sent to Professor Beard as well as several female journalists, including The Independent’s Grace Dent, Hadley Freeman of The Guardian and Time magazine’s Catherine Mayer.