Leading industry figures and experts believe that the nature and scale of the internet, as well as the status of those who provide access to the web, will make it impossible to enforce the rule.
They also point to a European directive, expected to come into force in Britain in the next two years, which defines internet service providers (ISPs) merely as conduits for information who cannot be responsible for content. This rule would seem to contradict the warning.
The Department of Health also came under fire for failing to consult the industry properly before sounding its warning and it is bound to be heavily criticised by civil liberties campaigners who will see the development as another attack on free speech.
ISPs have three main functions. They provide access to the web, so theoretically they could stop particular sites being reached. But they say that would not be feasible as it would require almost unlimited resources. And banning a site would give it notoriety prompting many more people to look at it. The British government also cannot try to shut down a foreign website at source because it would have no jurisdiction to do so.
The second main function of the ISPs is to provide "hosted web space" for websites. ISPs do have more control here, but even a small website may have 20 pages. So if an ISP hosted just 100 websites, it would have 2,000 pages to monitor.
Third, the ISPs provide news groups, or bulletin boards where articles can be posted. An article posted with an ISP's news group - for example, on adoption - will be picked up by linked news groups run by other ISPs worldwide. Checking everything on the news groups would be impossible.
What will particularly annoy the ISPs about the government's warning is that they are considered world leaders in self-regulation. ISPs are not licensed and do not have to register anywhere. But about 130 internet firms in the UK are members of the Internet Services Providers Association, which has been at great pains to provide a code of practice aimed at addressing the problem of illegal material. Formed in 1996, the Internet Watch Foundation (IWF) also works with the internet companies, the police and government, to tackle problems such as child pornography sites.
There appears to have been little consultation between the Department of Health and the industry. The IWF heard about what was afoot only when officials from other government departments began ringing it late last week.
Both the IWF and ISPA believe that the Department of Health's approach is flawed.
David Kerr, IWF's chief executive, said: "I think it's been generally accepted by ministers and the police that internet service providers don't and can't be expected to know what's on their servers. The department seems to be ignoring this basic point. This tactic is very unlikely to work and will put the department in conflict with the industry in the UK and in the rest of the world."
Mr Kerr said the industry had tried to stop material appearing on the web which would be illegal to publish in other forms in the UK - for example, child and extreme adult pornography. Although ISPs cannot monitor all the material passing through, once they are told about such material, they can remove it.
But another huge complication is the status of the ISPs. Many argue that they are not publishers but facilitators. The possible counter-argument, that they are indeed publishers because they own the servers carrying the material, has not been explored in the courts.
There are few precedents. Last year a New York lawyer sued the net firm Prodigy after an impostor sent obscene messages purporting to come from his 15-year-old son. The state's highest court threw out the claim, arguing that "an ISP, like a telephone company, is merely a conduit", and was backed by the supreme court.
Here, however, Mr Justice Morland decided in the high court that the internet company Demon Internet was liable for defamatory comments published about the physicist Laurence Godfrey - whose argument was that the ISP had become a publisher when it did not remove the comments.
Campaigners for free speech point out that some British ISPs now remove a comment, however fair and legitimate, as soon as they get a complaint rather than risk being sued.
Speaking after the Godfrey case, Mark Stephens, a media lawyer and vice-chair of the IWF, anticipated a flurry of litigation unless the laws were clarified. "In America ISPs have immunity over the content they provide access to and that must be the situation here. Otherwise, you'll have a legal free-for-all with libel writs flying left, right and centre."
He was right. A radical gay magazine's website, an anti-censorship site and one which highlighted miscarriages of justice, have all fallen victim to the uncertainty. Some have moved sites to the US rather than risk prosecution here.
One leading industry figure said: "It sounds as if the Department of Health has leapt into this without thinking the thing through. A lot of people in the industry are going to be puzzled and angry."
Mavrky Trust Law 2
Other Law Resources