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.
She reported them to the police after receiving "about 50 abusive tweets an hour for about 12 hours" and said she had "stumbled into a nest of men who co-ordinate attacks on women".
Ms Criado-Perez, from Rutland, told the BBC she had also tried to contact Twitter's manager of journalism and news, Mark Luckie, about the rape threats she was receiving, but he did not respond and locked his tweets to become private.
She said the form that allows Twitter users to report abuse was not adequate - particularly when such a high volume of abuse was being received. "Twitter need to be on the side of the victims," she said.
An online petition has been started in response to the abuse Ms Criado-Perez received calling for Twitter to introduce a "report abuse" button. It had been signed by more than 9,000 people by 15:00 BST on Saturday.
Kim Graham from Great Yarmouth, Norfolk, put the petition online at 09:00 BST after seeing abuse that Ms Criado-Perez had been getting. She told the BBC the "report abuse" button was something that came into her mind after finding it was "harder than it should be to report abuse".
The petition says: "Abuse on Twitter is common; sadly too common. And it frequently goes ignored. We need Twitter to recognise that its current reporting system is below required standards.
"The report abuse button needs to be accompanied by Twitter reviewing the T&C [terms and conditions] on abusive behaviour to reflect an awareness of the complexity of violence against women, and the multiple oppressions women face. It's time Twitter started protecting its users."
Ms Criado-Perez's cause has been supported by other prominent tweeters, including the journalists Caitlin Moran and Suzanne Moore and Independent columnist Owen Jones.
Ms Moran has called for a 24-hour Twitter boycott on 4 August to try to get Twitter to come up with an "anti-troll policy".
Labour MP Ms Creasy said: "This is not a technology crime - this is a hate crime. If they were doing it on the street, the police would act."
She told the BBC she had been chasing Twitter for the past 24 hours but they had not yet responded to her.
"I am absolutely furious with Twitter that they are not engaging in this at all," she said.
A Twitter spokesperson said: "The ability to report individual tweets for abuse is currently available on Twitter for iPhone and we plan to bring this functionality to other platforms, including Android and the web.
"We don't comment on individual accounts. However, we have rules which people agree to abide by when they sign up to Twitter. We will suspend accounts that once reported to us, are found to be in breach of our rules.
"We encourage users to report an account for violation of the Twitter rules by using one of our report forms."
The general manager of Twitter UK, Tony Wang, later tweeted that the company was "testing ways to simplify reporting, e.g. within a Tweet by using the 'Report Tweet' button in our iPhone app and on mobile web".
A Metropolitan Police spokesman confirmed that "officers from Camden have received an allegation regarding comments made via a social network, that was reported on 25 July".
He added that "inquiries continue" but so far there had been "no arrests".
There have been some high profile arrests related to celebrities abused on Twitter, including a teenager arrested over the abuse of Great Britain's Olympic diver Tom Daley.
Guidelines published by the Director of Public Prosecutions Keir Starmer in June said there should be a "high threshold for prosecution in cases involving communications which may be considered grossly offensive, indecent, obscene or false".