The Prime Minister said people convicted of extremism will be banned from working with children.
David Cameron also announced powers to remove passports from 16-17 year-olds who are thought to be at risk of radicalisation.
In a statement in response to David Cameron's speech this morning Andrea Williams, Chief Executive of the Christian Legal Centre, said: "The government's Counter-Extremism Strategy betrays a dangerous blindness to the Christian basis of 'British values' and a naivety about the nature of Islamic radicalisation.
"The government is right to recognise the danger that Islamic radicalisation poses to freedom but the government's response poses dangers of its own.
"The strategy as a whole is incoherent. It states, for example, that extremism disruption orders will not prevent people from expressing their religious beliefs, yet it is clear elsewhere in the strategy that the censoring of certain religious beliefs is exactly what the government wants to achieve."
She added that: "We remain very concerned, for example, by the proposals for 'extremism disruption orders'.
"The definition of extremism, and especially 'non-violent extremism', remains dangerously vague and open-ended. Despite the protestations of government ministers, it casts the net far too wide.
"The severe curtailment of a person's civil liberties could hang on this definition. It cannot possibly be left so vulnerable to future interpretation and manipulation.
Andrea Williams concluded by saying: "In its current form, this strategy represents a major challenge to the freedom of Christians and many others."
A Christian expert in Islamic affairs has also told Premier that new rules on extremism in the UK will not work.
Dr Antony McRoy, expert in Islamic affairs, told Premier's News Hour that this is too little, too late: "It's a bit like trying to shut the barn door when the horse has already bolted, and again how many of those young people who've gone have actually told their parents, and how many of those parents say they actually suspected?
"I really don't think it's going to work."
He added that: "Anyone who's gone to Islamic State is a traitor, who represents a continuing threat to the United Kingdom, and no amount of preventative strategy or having educational indoctrination - which the Prime Minister's suggesting basically - is going to work."
But the Home Secretary Theresa May says it is not just about Islamic State but also about far right Neo-Nazis and others promoting messages of hate and division.
Listen to Premier's Marcus Jones speaking to Dr Antony McRoy here:
