Mr Hemming said it was no longer practical for Giggs' name to be kept out of the public arena as so many people were now aware who he was, due to Twitter and other social networks.
"With about 75,000 people having named Ryan Giggs on Twitter it's obviously impractical to imprison them all," said Mr Hemming.
The MP was immedately rebuked by the Commons Speaker who said it was 'not the occasion' to raise such issues.
Mr Hemming retaliated, however, saying he wished to clarify the enforcibility of a law which 'clearly does not have public consent'.
The identification came just hours after the High Court had refused to allow journalists to name Manchester United player Giggs, who was alleged to have had a sexual relationship with reality TV star Imogen Thomas.
Mr Justice Eady rejected a fresh application by News Group Newspapers to discharge the privacy injunction relating to Giggs, who is married, on the basis that to continue it would be "futile", given recent widespread publicity about his identity.
The judge said: "It has never been suggested, of course, that there is any legitimate public interest, in the traditional sense, in publishing this information.
"The court's duty remains to try and protect the claimant, and particularly his family, from intrusion and harassment so long as it can."
Meanwhile, a Times journalist who it was claimed was facing contempt of court proceedings over naming on Twitter another Premier League player with a privacy injunction over an alleged affair, was also named as by Mr Hemming in the Commons as columnist Giles Coren.
Earlier, the Prime Minister David Cameron said privacy rulings that prevent newspapers printing stories already in the public domain, in which he appeared to be alluding to the Giggs case, are “unsustainable” and “unfair”.
Mr Cameron said the Government would look at the issue of super-injunctions but once again warned judges that it was Parliament’s job to create law.
Speaking to ITV1's Daybreak, Mr Cameron indicated that he knew the identity of the footballer with the injunction, "like everybody else".
Giggs, referred to as CTB in court documents, is alleged to have had a "sexual relationship" with former Big Brother contestant Miss Thomas.
Despite thousands of Twitter users openly discussing his identity and one Scottish newspaper even publishing his picture on its front page on Sunday, publications in England and Wales remain prevented in theory from naming by a draconian court injunction.
Mr Cameron said: "It is rather unsustainable, this situation, where newspapers can't print something that clearly everybody else is talking about, but there's a difficulty here because the law is the law and the judges must interpret what the law is.
"What I've said in the past is, the danger is that judgments are effectively writing a new law which is what Parliament is meant to do.
"So I think the Government, Parliament has got to take some time out, have a proper look at this, have a think about what we can do, but I'm not sure there is going to be a simple answer."
Mr Cameron will set up a new committee to look at the use of gagging orders in controversial privacy cases, the Attorney General said today.
Attorney General Dominic Grieve QC said the Prime Minister will make the recommendation in a letter to John Whittingdale, chairman of the Culture, Media and Sport Committee.
Yesterday Giggs was identified in Scotland by the Sunday Herald which claimed it was outside of the jurisdiction of the injunction.
Initially it was thought Mr Grieve might start proceedings against the newspaper for contempt of court after it emerged that copies of the paper were available in England.
But Scottish First Minister Alex Salmond warned that such a course of action would be "extremely foolish".
"I think it would be very, very unlikely that an Attorney General would be as foolish as to do so," he told the BBC Radio 4 Today programme.
"I think the political issue is whether it is tenable to pursue this sort of injunction.
"I would have thought there is an increasing view it is untenable to do so. There is a whole question of what is of interest to the public and what is in the public interest, which can often be different things.
"But the law essentially is a practical thing. It looks to me like English law and English injunctions are increasingly impractical in the modern world."
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