Opponents of the provision, however, warned that it would curb free speech.
The Terrorism Act 2006 allows groups or organisations to be banned for glorifying terrorism and distributing publications promoting terrorist acts.
The most controversial element of the act, allowing terror suspects to be detained without charge for up to 28 days instead of 14, will come into force later this year.
The law was drafted after bombers killed 52 commuters and themselves on the London transport system last July.
It was given greater urgency earlier this year when demonstrators in London condemned the publication in several European newspapers of cartoons depicting the Prophet Muhammad by calling for those who insulted Islam to be beheaded.
But the legislation struggled to pass through parliament as critics said it was too wide-ranging and would be unworkable and an erosion of free speech.
Blair: Law was needed to enforce
fight against terrorism
The upper House of Lords rejected the bill several times before eventually backing down.
Tony Blair, the prime minister, has said the new law was needed to show Britain would not waver in its fight against terrorism.
But critics complain it is too vague, arguing that current laws do the job just as well.
Human rights group Liberty said it was worried the legislation would outlaw "passionate speech", criminalise non-violent political parties and "make Britain less safe by silencing dissent".
Gareth Crossman, the policy director, said: "These new powers make us not only less free, we are also less safe when we drive dissent underground and alienate minorities."
He noted that people who protest against hardline rulers such as Robert Mugabe, the Zimbabwean president, could be deemed as criminals.
John Falding's girlfriend Anat Rosenberg was killed during the July 7 London attacks.
"These new powers make us not only less free, we are also less safe when we drive dissent underground and alienate minorities"
Policy director, Liberty human rights group
He told BBC Radio he thought the new laws were a public-relations exercise.
"Most of the (new) provisions are covered by existing legislation and my first thought was that this was just a bit of public relations by the government," he said.
"Suddenly we have this grand new anti-terrorism act. But then, when I look more closely at the provisions and see how widely they're drawn, I think there must be another agenda here.
"It's so catch-all. Ally this to other measures that the government have taken throughout the civil liberties field and I started to get concerned - and I don't feel reassured that this is going to help us much in the fight against terrorism."
Last November, Blair suffered his first parliamentary defeat since coming to power in 1997 after MPs rejected a bid to increase the maximum period security suspects can be held without charge from 14 to 90 days.
MPs eventually backed the 28-day limit.