Twitter executives are to be invited to give evidence to MPs as uncertainty over the future of privacy issues continues.
The Commons' culture, media and sport committee chair John Whittingdale has been charged with investigating the issue by prime minister David Cameron.
It follows the recent spate of controversial revelations on the microblogging site, which has seen anonymous users break superinjunctions protecting celebrities' privacy.
Twitter bosses have confirmed they are prepared to hand over the details of users to law enforcement agencies.
The first case of this taking place follows legal action by South Tyneside council in a California court. Twitter is understood to have handed over the user details of five accounts which South Tyneside council claims had issued defamatory statements.
"I would have thought we would certainly want to hear from Twitter," Mr Whittingdale told the Independent.
"Twitter has an ethical policy and they respect laws in each jurisdiction so I thought they would want to come."
Meanwhile John Hemming, the Liberal Democrat MP who used parliamentary privilege to break the superinjunction protecting Manchester United footballer Ryan Giggs, stepped up his attack on judges in a blog post.
Responding to a fresh list of injunctions on Twitter, which he insisted he did not support, he said it was hard to combat those who used anonymity and posted tweets outside England and Wales' jurisdiction.
Tackling these "would involve effectively cutting the UK off from the rest of the world for many websites", he explained.
Mr Hemming concluded: "We are in a position whereby either reality needs to be changed to fit the law or the law needs to be changed to fit reality.
"Personally I am one for the latter. I don't think that criminalising gossip is the way forward nor do I agree with producing a technological solution to give a form of Chinese censorship of the internet as appears to be the preferred solution of the judiciary."