Twitter is facing a barrage of criticism after a journalist and feminist blogger who campaigned for Jane Austen to become the new face of the £10 note was subjected to a series of rape threats.

Caroline Criado-Perez, a freelance journalist who co-founded thewomensroom.org.uk and the Week Woman blog, and fellow campaigners were delighted last week when the Bank of England confirmed that the Pride and Prejudice author would replace Charles Darwin on the notes, probably in 2017.

But Criado-Perez quickly found herself subjected to a sustained campaign of abuse on Twitter, of the type that MPs say should become a criminal matter.

Writing in the Observer, Labour MP Stella Creasy condemned the threats and called for action from both Twitter and its users to push back against online aggression towards women.

"This is about more than making Twitter somewhere fun for everyone to enjoy," she said. "If we want a world where everyone can live hassle-free, then everyday expressions of inequalities need to be confronted – not least as they help ease the big inequalities."

Fellow Labour MP Steve Rotheram tweeted that "hopefully those responsible will be receiving a knock on the door from their local constabulary".

By Saturday afternoon more than 9,000 people had signed an online petitioncalling on Twitter to add an abuse button for those threatened with sexual violence and to make the site responsible for any criminal threats posted on it.

The petition claims: "During a 12-hour period, Caroline Criado-Perez was targeted repeatedly with rape threats. Caroline attempted to stir a response from Twitter's Mark S Luckie. His response was to lock down his account."

Many who have signed the petition have questioned why the online community appears to be subject to different laws from the real one. "This is criminal behaviour in the real world; why should people get away with it on Twitter?" one supporter wrote.

Another added: "Rape threats are a criminal offence in real life. They should not be allowed in cyberspace."

A number of high-profile names have lent their support. The writer Caitlin Moran tweeted: "For those who say, 'why complain – just block?' – on a big troll day, it can be 50 violent/rape messages an hour. Exhausting and upsetting."

The comedian Dara Ó Briain warned that Twitter faced an exodus of users if such messages continued to be disseminated. He tweeted: "If the ladies leave twitter because of all the dumb, rapey 14-year-old boys, then I'm outta here people. Like most grownup men too, I'd say."

Criado-Perez said she had been overwhelmed by support: "Lots of people are saying how inspired they feel by my stance on this."

She said it was important to confront those who used rape threats. "We need to get rid of the idea that you don't feed the trolls. Someone issuing rape threats wants women to shut up and get off Twitter ... We can't let them win."

Significantly, it appears that Criado-Perez was the victim of a sustained and co-ordinated attack. Initially, she was the subject of several offensive tweets, but these died away after about a day. She was then subjected to hundreds of tweets, which suggests that she was targeted by a group of Twitter users.

Criado-Perez believes the affair has highlighted Twitter's inability to respond to such attacks. "If you get an abusive message, you can fill in an online form and make a complaint," she said. "But if you're subject to hundreds of tweets it's not practical … Twitter does not understand the nature of abuse online."

Twitter UK general manager Tony Wang said the company takes online abuse seriously. He tweeted: "We encourage users to report an account for violation of the Twitter rules by using one of our report form. Also, we're testing ways to simplify reporting, eg within a tweet by using the "Report Tweet" button in our iPhone app and on mobile web. We will suspend accounts that, once reported to us, are found to be in breach of our rules."