The issue is on the agenda at the G8 summit in Deauville in northern France this week as the political fallout from the outing of the Manchester United star as the footballer who has a gagging order continues.
Deputy Prime Minister and LibDem leader Nick Clegg criticised one of his own MPs for using parliamentary privilege to reveal the name, warning that no-one was above “the rule of law”.
A leading lawyer, Geoffrey Robertson, QC, also called on Parliament to investigate the MP, John Hemming, amid claims that he abused the rules.
However, Mr Hemming defended himself, saying that the player’s name was already in the public domain even before he said it in the House of Commons on Monday.
Giggs was named just 24 hours after the Sunday Herald revealed his identity to readers in Scotland but not England. He had been the subject of a mass protest over the weekend on Twitter, after it emerged that he was suing the micro-blogging website.
Twitter itself has faced accusations that it was making a mockery of the law after tens of thousands of people apparently breached the court order preventing the identification of Giggs.
The Government has ordered a rush review of the law surrounding super-injunctions, which the Prime Minister has described as “unsustainable”.
A number of peers have called for the review to consider the potential to control social networking websites, as well as the battle between privacy and free speech.
French President Nicolas Sarkozy, meanwhile, has pressed for the laws surrounding the web to be included on the G8 agenda. He is pushing for tighter regulations, insisting that it would be wrong for governments not to get involved in the technology.
A number of delegates from internet companies will attend the summit to take part in the session with global leaders.
However, it is thought that Twitter will not be among them, despite being one of the most high-profile web firms in the world.
The Prime Minister’s official spokesman did not rule out that Giggs and the current row over the role of the internet in breaking court orders could come up at the meeting, describing the discussion as “free flowing”.
However, it is not thought that any firm decisions on regulation will be made at the summit.
Mr Hemming told MPs yesterday that questions had been raised about whether he should have named the player.
In a staunch defence of his actions, he said: “I’m not a party to the privacy case, I’m not being served with the injunctions, I haven’t actually seen the injunctions and cannot guarantee that it actually exists.
“I’ve read his name in the Sunday Herald, I’ve read his name in Wikipedia, I’ve read his name on Twitter. I can honestly stand on a soap box and say what I said in the House of Commons in Scotland.
“I believe I could probably say it on Hyde Park Corner because it is in the public domain.
“For me to have abused parliamentary privilege I would have to use it in the first instance.
“I do not think the case has been made that in fact it would have been contempt of court outside this House.”
Even before Mr Hemming rose to speak, Deputy Speaker Lindsay Hoyle said he had been asked by Speaker John Bercow to remind him of the ruling given by him yesterday “in which he strongly deprecated the abuse of parliamentary privilege to flout an order or score a particular point”.