New laws making it illegal to glorify terrorism and distribute terrorist publications have come into force.
New police powers on detention are delayed
The Terrorism Act 2006 allows groups or organisations to be banned for those offences and covers anyone who gives or receives training.
The act designates nuclear sites as areas where trespass can become a terrorist offence.
Human rights campaigners argue the law is drawn far too widely and it faced stiff opposition in the House of Lords.
Peers were worried it would curb free speech and rejected the plans five times before voting them through in March.
Liberal Democrat and Conservative MPs voted against the Terrorism Bill, saying existing legislation already covered the glorification offence.
The bill was introduced after 7 July bomb attacks in London, and Prime Minister Tony Blair said the new law would allow action to be taken against people glorifying those attacks.
People had held placards praising the 7 July bombers during protests in London against cartoons satirising the Prophet Muhammad.
The act also creates new offences of undertaking terrorism training, preparation or planning of a terrorist act and disseminating terrorist publications.
Plans to double the amount of time suspects can be held without charge to 28 days will come into force later after consultation with police chiefs.
The government wanted police to be allowed to hold suspects for up to 90 days, although MPs rejected this proposal.
Shadow Home Secretary David Davis said the Tories welcomed the much of the new act, but said there were "concerns" over the rules on glorification.
"During the passage of the bill we secured an assurance from the government that this would be revisited," he said.
Doug Jewell, of the human rights group Liberty, told the BBC the rules on glorification were "too broad".
He said: "Anyone supporting violence to remove a regime anywhere in the world now or in the past would theoretically get caught up."