The bill will also place a statutory duty on schools, colleges, prisons and local councils to help prevent people from being drawn into terrorism, the home secretary said.
She said universities would have to show that they have put in place policies to deal with extremist speakers.
“The organisations subject to the duty will have to take into account guidance issued by the home secretary. Where organisations consistently fail, ministers will be able to issue directions to them “which will be enforceable by court orders”, May announced.
She said: “We are engaged in a struggle that is fought on many fronts and in many forms. It is a struggle that will go on for many years. And the threat we face right now is perhaps greater than it ever has been. We must have the powers we need to defend ourselves.”
The home secretary confirmed that the new counter-terror law would include powers to exclude from the UK British citizens suspected of involvement in terrorism-related activity abroad. Their travel documents will be cancelled and their names placed on no-fly lists for up to two years.
In a speech at Rusi, the defence thinktank, May said: “The new powers will help us to prevent radicalisation, strengthen the Tpims [terrorism prevention and investigation measures] regime, give us greater powers to disrupt and control the movements of people who go abroad to fight, improve our border security, make sure British companies are not inadvertently funding ransom payments, close down at least part of the communications data capability gap, and establish a new independent privacy and civil liberties board.
“This legislation is important. The substance is right. The time is right. And the way in which it has been developed is right. It is not a knee-jerk response to a sudden perceived threat. It is a properly considered, thought-through set of proposals that will help to keep us safe at a time of very significant danger. It builds on a successful strategy. It goes with the grain of existing policy. It has been drawn up in close consultation with the police and security services. It is deliberately focused on practical measures that we can be confident will work. And it broadly commands cross-party support.”
May said the police had foiled 40 different terrorist attacks in the last 10 years, including a planned Mumbai-style gun attack, an attempt to bring down a plane, the attempted assassination of an ambassador and the planned murder of members of the armed forces.
She said there had been 753 counter-terrorism arrests, 212 people charged, 148 convicted, and 138 now in prison since May 2010. Hundreds of people had been excluded from Britain, including 61 people on the grounds of national security and 84 hate preachers. She has also revoked citizenship from 27 people on terror grounds.
The home secretary said the bill would not be treated as emergency legislation but would be fast-tracked through parliament before the general election.
The detailed proposals include:
• Putting the Channel anti-radicalisation programme on a statutory basis to improve its delivery.
• A new statutory duty on colleges, schools, prisons, probation providers, police and councils to prevent individuals being drawn into terrorism. Ministers will have powers to issue directions to organisations that repeatedly invite extremist speakers or fail in the duty in other ways.
• Reforming the Tpims measures regime so that suspects can be relocated to a different part of the country. The threshold for issuing a Tpim is to be raised to the civil standard of proof of “reasonable balance of probabilities”.
• Police are to be given the power to seize passports and travel documents, including tickets, for up to 30 days, from people thought to be leaving UK to engage in terrorism-related activities. This will apply to British citizens as well as others.
• New temporary exclusion orders for British citizens suspected of being involved in overseas terrorism to prevent them returning to the UK. They will be placed on no-fly lists.
• Airlines that fail to supply passenger lists in advance will be prevented from landing in Britain.
• A new criminal offence will be created to make it illegal for British insurance companies to provide cover for terrorist ransom payments.
• A requirement for internet service providers to retain data on internet protocol addresses to allow individual users to be identified.
• A new civil liberties and privacy board will be set up to support the work of David Anderson QC, the independent reviewer of terrorism laws.