A petition calling on Twitter to add a "report abuse" button has received thousands of signatures.
It follows a deluge of abuse and rape threats received by Caroline Criado-Perez, who successfully campaigned for women to be included on UK banknotes.
MP Stella Creasy told the BBC she was "furious" Twitter had yet to do anything about Ms Criado-Perez's abuse.
Twitter UK's Tony Wang said the company was "testing ways to simplify" reporting abuse.
Ms Criado-Perez, who had appeared in the media to campaign for women to feature on banknotes, said the abusive tweets began the day it was announced that author Jane Austen would appear on the newly designed £10 note.