Labour MP Stella Creasy and feminist campaigner Caroline Criado-Perez have received fresh death and rape threats, as the campaign of attacks on Twitter against women who highlight online abuse continues.

One user, calling themselves @killcreasynow made specific death threats against the MP and detailed graphic sexual violence. The same user also threatened to kill the Conservative MP Claire Perry, who has been targeted following her high-profile campaign to restrict access to pornography online.

The account made a series of threats before being suspended after about 30 minutes.

Minutes later, another account – @eatcreasynow – that claimed, and appeared, to have been set up by the same user continued to attack Creasy with rape threats, including specific times. That account was also suspended but highlights the difficulties Twitter is having in dealing with this issue, as users can just set up new accounts when suspended.

Creasy retweeted some of the sinister messages to her 30,000 followers as she said the "morons" behind the abuse would face justice.

Police said on Monday night that they were investigating a series of sexually explicit and violent tweets sent to Creasy after she spoke out in support of Criado-Perez. Criado-Perez received a barrage of abuse following her successful campaign to have a woman's picture placed on a new banknote.

Scotland Yard said: "Officers in Waltham Forest received an allegation of malicious communications from an MP. The allegation relates to comments made on Twitter and is currently under consideration."

The latest attacks on Creasy came as Criado-Perez, who was also subjected to more abuse and threats overnight, appeared on Newsnight.

Criado-Perez, a freelance journalist, organised a campaign that included a petition signed by more than 35,500 people after the Bank of England decided to replace Elizabeth Fry with Winston Churchill on new £5 banknotes.

Her campaign led to the announcement that Jane Austen would feature on the new £10 note from 2017, but prompted a litany of hostile and menacing tweets against her.

Criado-Perez described how the abuse had left her feeling under siege and terrified in her own home. She told Newsnight: "It has consumed my life both physically and emotionally. I've not really had much sleep.

"The threats have been so explicit and so graphic that they've sort of stuck with me in my head and have really put me in fear, I realised."

But in a defiant message to her tormentors, she said: "I would like to say I think they are completely pathetic. If they think they are going to drive me or any other woman off the internet they are going to be sorely disappointed."

She criticised the response from Twitter and claimed to have been blocked by Mark Luckie, one of its senior managers, after he was made aware of her ordeal. "I can't begin to imagine why, either from a decent human being perspective or just from a PR perspective. I would imagine Twitter is pretty embarrassed about that."

Police have questioned a 21-year-old man in connection with the torrent of abuse. He has been bailed to a date in mid-September following his arrest in Manchester on suspicion of harassment offences, Scotland Yard said.

It follows a complaint made on Thursday to detectives in Camden, north London, who are continuing their inquiries, the force added.

Critics have called for Twitter to take faster and stronger action against online thugs and Creasy has criticised the micro-blogging site's security policies. She told BBC Radio 4's The World At One: "This is not about Twitter, this is about hatred of women and hatred of women who speak up. And indeed, some of those people sending the messages have been absolutely explicit about that.

"Twitter needs to be explicit that sexual violence and sexual aggression will not be tolerated as part of their user terms and conditions.

"We can all challenge these people and indeed when this happens to me in other occasions I tend to retweet it so people can say: 'This is not acceptable.'

"But we also need a platform for when things are not dealt with by users, when actually users do not realise that they are being misogynist, they are being aggressive or that actually they are trying to shut other people's free speech down."

She continued: "I think we are evolving how we understand the impact of the internet and social media on crime and how it's committed. But let's be very clear, this isn't about free speech.

"Free speech is incredibly important on and offline, but it's not free speech for someone to be threatened with rape. We have to have ways of dealing with that and we mustn't misunderstand the level of cyberharassment taking place in this country.

"That's what we are looking for Twitter to play a key role in because actually if Twitter didn't exist, these people would still propagate these kind of views."

The chairman of the Association of Chief Police Officers communications advisory group, which leads on social media for police forces, said Twitter had more work to do in combating online threats.

Andy Trotter said he feared a whole new tranche of web-based hate crimes could "cause great difficulty for a hard-pressed police service" trying to deal with what could amount to thousands of allegations.