But the providers argue they already do all they can to fight illegal terrorist material online, and experts say even powerful filters cannot block determined users from getting their message out.
"Fundamentally, it's a losing proposition," said Ian Brown, a research fellow at the Oxford Internet Institute, noting that even countries such as China and Myanmar have had trouble with their online censorship efforts.
The prime minister's proposal comes as the European Union considers ways to sanction Web sites that display terror propaganda or recruit for terrorist groups.
Addressing lawmakers, the prime minister said Home Secretary Jacqui Smith was "inviting the largest global technology and Internet companies to work together to ensure that our best technical expertise is galvanized to counter online incitement to hatred."
Smith, giving the keynote speech at a conference on radicalization and political violence on Thursday, said "the Internet is not a no-go area for government." She compared her government's plan to counter extremism on the Internet to its long-standing campaign against pedophiles and child pornography online.
"If we are ready and willing to take action to stop the grooming of vulnerable young people on social-networking sites, then I believe we should also take action against those who groom vulnerable people for the purposes of violent extremism.
"Where there is illegal material on the Net, I want it removed," she said.
But how? And who would do the removing? Smith did not go into details, saying only that she was working closely with the communications industry. Service providers, for their part, were not enthusiastic.
Britain's Internet Service Provider Association, which represents major service providers such as BT Group PLC and the U.K. arms of Time Warner Inc.'s AOL and Yahoo Inc., said the most troublesome Web sites were hosted abroad, where the government's writ did not carry in any case.
And even if sites suspected of inciting terror were hosted in Britain, the ISPA said its members had neither the competence nor the desire to rule on whether a particular site was illegal.
Attempts to do so, the group said, amount to corporate censorship and could subject service providers to lawsuits and accusations of breaking free-speech laws.
Unlike the case with child pornography, which is often easily recognizable by sight, policing terror-related Web sites requires subjective judgments on whether a foreign-language text was inciting anything or anyone, the ISPA contends.
Hear Larry Magid's Podcast interview with John Carr, an online security advisor to the U.K. government
The Home Office said it would meet leading British Internet service providers to examine ways of curbing online propaganda, but said Brown's plan had not yet been considered in detail. Not clear, for instance, was whether the plan would require new laws or different ways of enforcing existing regulations.
British law already forbids the publication of statements likely to be seen as encouraging terrorism or the dissemination of terrorist material, such as bomb-making information, according to the Internet Watch Foundation, an EU-funded body that works with the British government to monitor and remove illegal online content.
Last week, a British court ruled that radical Muslim cleric Abu Hamza al-Masri can be extradited to the United States to face trial on charges of supporting terrorism.
In the U.S., he is charged with trying to establish a terrorist training camp in Oregon, conspiring to take hostages in Yemen and facilitating terrorist training in Afghanistan. British media report that al-Masri faces a total of 11 charges in the U.S., which carry a maximum penalty of 100 years in prison.
The presiding judge in the U.K. said the case would now be referred to Home Secretary Jacqui Smith for a final decision.
Under Britain's present "notice and take down" procedures, authorities, companies and individuals can demand that Internet service providers remove content considered to be unlawful. That includes child pornography, as well libelous, obscene or terrorist material, according to Internet Watch Foundation.
Although the removal of child pornography is relatively uncontroversial, service providers have expressed unhappiness at having to shut down their customers' sites over, for example, allegations of libel, where guilt is difficult to determine at a glance. They are unlikely to welcome similar demands over material that allegedly glorifies terrorism.
Besides taking down their own customers' sites, service providers also might be pressured to block ones hosted abroad. The government might draw up a list of banned sites, similar to one the Internet Watch Foundation has maintained since 2004 and updates twice daily to block Britons from visiting child pornography sites hosted overseas.
Another method might be to persuade search engines like Google Inc. or Yahoo Inc. to filter out prohibited content from their search results, or manage their searches so that the words "bomb," "al Qaeda," or "video" did not lead users to terrorist-related sites.
But both these measures would do little to deter the computer-literate youth being targeted by al Qaeda, Ian Brown said. He noted that users could still swap terror-related content through file-sharing networks, discussion forums, or access material through sophisticated proxy servers and programs that allow users to browse the Net anonymously.
Efforts to use Internet service providers to police online content amounted to a "censorship proposal" and was bound to be problematic, said John Gage, vice president and chief researcher for Sun Microsystems Inc.
"It's one of these things that's going to be very difficult to implement," he said.