Over 30,000 Twitter users have signed a petition calling for the site to implement a “report abuse” button.
The campaign started after a man was arrested for repeatedly threatening to rape a user of the social networking site.
Twitter has been criticised for its slow response to the abuse faced by Caroline Criado-Perez – who successfully campaigned for the image of a woman to be out on a new banknote.
Show home secretary Yvette Cooper wrote a letter to Twitter’s UK general manager Tony Wang in which she called the site’s response to the threats “extremely weak” and “inadequate”.
A 21-year-old man has been arrested in connection with the abuse aimed at Criado-Perez, but the campaigner says she has many more threats to report.
This is not the first time Twitter trolling has turned into a high-profile case. Last year a man was jailed for 56 days after posting a series of offensive when footballer Fabrice Muamba collapsed during a match. Another man who sent racial abuse to Stan Collymore via Twitter was also sentenced last year.