Max Hill, appointed by the government to review terrorism laws, also urged that activities that had not yet become acts of terrorism, such as thinking about terrorism, should not be treated as criminal.
"We do not, and should not criminalise thought without action or preparation for action. Thought with steps towards action can be terrorism. Thought without action or preparation for action may be extremism, but it is not terrorism," Hill said in a speech to human rights group Justice this week.
Hill, a barrister, also advised that the government must take a more proactive role to speak to and engage with Muslim communities.
"We, as a nation, must not be terrified, nor must we allow our Parliament to enact measures that might make things worse not better," he said.
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His views attracted a mixed response, with UK Attorney- General Jeremy Wright saying that new anti-terror laws were required.
The Downing Street said in a statement: "As we have seen painfully in the UK this year, we face an unpredictable threat from terrorism. We have to tackle the ideologies that drive or inspire these kinds of attacks.
"That is why we are doing things like establishing a new commission on countering extremism to help expose all forms of extremism and division and to challenge those who preach hate.
"What we want to do is to send a clear message that we will not tolerate terrorism, those who help radicalise terrorists with their extremist views, or those who turn a blind eye to terrorist activity.