British values will prevail in the fight against extremism, Home Secretary Theresa May said as she set out a raft of new measures to tackle radical and terrorist elements in Britain.

Under the plans which will feature in the Tory election manifesto, new "banning orders" would allow the authorities to outlaw extremist groups, even if they did not pose a terrorism threat.

Hate preachers could be targeted with "extremism disruption orders (EDOs)", which would allow the courts to restrict the movement and activities of individuals to prevent the risk of violence or public disorder.

It has been reported that posts by extremists on social media such as Twitter and Facebook will also be the target of controls.

In addition, Mrs May launched a cross-government counter-extremism strategy that will move away from the "hard end of the extremism spectrum" and will tackle not only Islamist extremists but neo-Nazis and other hardline groups.

The Home Secretary spoke of the importance of standing up for the nation's values and fighting extremism and bigotry in all forms even if it is not violent because "the damage extremists cause to our society is reason enough to act".

Tory sources said the strategy could prevent help prevent a repeat of the so-called Trojan Horse plot, which saw schools in Birmingham fall under the influence of Muslim fundamentalists.

Mrs May said Muslims in the UK are free to exercise their right to freedom of conscience, thought and religion but must realise that living in the country comes with responsibilities to respect British values.

She told the Tory Party conference: "You don't just get the freedom to live how you choose to live, you have to respect other people's right to do so too and you have to respect British values and institutions - the rule of law, democracy, equality, free speech and respect for minorities.

"These are the values that make our country what it is. These are our values. There is no place for extremism here."

She went on: "Those extremists are dangerous but they are a small minority. We know the overwhelming majority of British people want to be free - free from danger, free from fear, free from prejudice, free from discrimination, free to practise their religion, free to observe their cultures and traditions, free to dress as they like, free to be educated as they choose, free to work where they wish, free to live with whom they love, free to raise their families as they see fit, free to get on with their lives.

"We must not become a society where these things are no longer possible. We must confront segregation and sectarianism. We must face down extremism in all its forms. We must stand up for our values. Because, in the end, as they have done before, those values, our British values, will win the day, and we will prevail."

The Home Secretary said the potential for Britons to become radicalised at home before joining Islamic State (IS) terrorists in Iraq and Syria and then returning to the UK was clear and so new powers were needed.

She said banning orders would help the authorities tackle groups that are not covered by existing terror laws while extremist disruption orders would tackle those "who stay just within the law but still spread poisonous hatred".

Mrs May also revealed that she has so far removed the passports of 25 Britons seeking to travel to Syria, while 103 people have been arrested in relation to terrorism in Syria.

Of those arrested 24 have been charged and five convicted, she said.

The Home Secretary also committed to include tougher surveillance powers for the security services in the Tory manifesto as their ability to obtain the data is declining "rapidly and dangerously".

Mrs May said that in six months the National Crime Agency dropped at least 20 cases as a result of missing communications data, 13 of which involved a threat to the life of a child, while the Metropolitan Police over a three month period had to drop 12 cases including sexual offences and potentially life threatening scenarios relating to a "suicide threat" and a kidnap.

She said: "The solution to this crisis of national security was the Communications Data Bill. But two years ago, it was torpedoed by the Liberal Democrats. I'm told that the Lib Dems now tell the newspapers that 'they might have to give ground on surveillance powers in a future coalition government agreement'.

"But they also say that they have 'no intention of allowing changes before the general election'.

"This is outrageously irresponsible, because innocent people are in danger right now.

"If we do not act, we risk sleepwalking into a society in which crime can no longer be investigated and terrorists can plot their murderous schemes undisrupted. We have to give the police and the security services the powers they need to keep us safe. And that is what the next Conservative government will do."

Prime Minister David Cameron said that the package could involve a broadcasting ban on extremist preachers, similar to that imposed on Sinn Fein politicians in Northern Ireland in the 1980s.

Mr Cameron told Channel 4 News: "The historians can argue about how it worked in Northern Ireland, but this is different.

"What we are proposing here is to look at groups who currently are just the right side of not endorsing actual violence but they are preaching extremism.

"There's a very strong argument to say that these extremists are poisoning the minds of young people who are then going on to become violent, and we shouldn't give airtime, we shouldn't give freedom, to these sorts of groups."

The PM said that action was already being taken to remove extremist messages from the internet: "We take down thousands of pages of extremist literature and videos from the internet - those gruesome, ghastly beheading videos, we take them down.

"You could make the argument 'It's hopeless, you can't do anything, just sit back and let all this wash over you', I don't accept that. I think we have to combat not just violent extremism, but we have to combat extremism as well."

Mr Cameron told interviewer Jon Snow: "I don't want to name names but I think you've probably had on your programmes those people who perhaps go just one stop short of endorsing violence, but they are really inciting young British people into hatred that is leading to violence.

"We don't just say Combat 18 is a bad thing, we think the National Front is a bad thing too, and we have to be as confrontational with this Islamist extremist terror."

Tory former shadow home secretary David Davis expressed concern about the plans.

The MP for Haltemprice and Howden told the BBC: "These are quite incredible powers to limit democratic rights, rights that people have had for 200 years in this country, and they are based on the Home Secretary having a reasonable belief - that's the test, not an evidential test, a reasonable belief - that an organisation will break certain criteria.

"And one of the criteria is a risk of harassment, alarm or distress. Well, one's tempted to say I do that to the Tory Party every day. This is really, really serious stuff.

"I think it will have real trouble both getting through the House of Commons and indeed real difficulty standing up in front of the court."

He added: "Deal with the violence, deal with the actions, deal with the measures. We didn't stop a whole load of people leaving here to go to Syria. Why didn't we do that? Those are the ways you deal with these things."

He went on: "We've got to be very careful that we don't end up like the people we're trying to defeat, forgetting what we're defending. We're defending a liberal democracy, one in which you can say all sorts of things."

Former attorney general Dominic Grieve QC said the "devil lies in the detail" of the proposals.

He told BBC Radio 4's World At One programme: "If one introduces measures which may be perceived as draconian or restrictive on other people's liberties, then this can have the unintended consequence of not actually tackling correctly the problem which is arising, but simply fuel resentment, and it's a very delicate balancing act between these two concepts that we have to pay attention to."

He added: "It's difficult to see how in practice some of these restrictions would operate without leading to the consequence that a person would end up being prosecuted for expressing a point of view which the Home Secretary has considered is extreme."

Mr Grieve stressed he was "open-minded" and "would look at them very carefully", adding: "But I think any restriction on freedom of expression of individuals outside of the criminal law is something that has to be approached with very great caution."