Lord Blair, the Commissioner of the Metropolitan Police at the time of the 7/7 bombings, has suggested David Cameron is wrong to try and take a tougher approach to conservative Islam.
In the wake of the terror attack in Tunisia in which at least 29 Britons are confirmed to have been killed, the prime minister said Britain should be more "intolerant of intolerance".
However an an interview with BBC Newsnight on Wednesday evening, Blair said fundamentalism was "in itself is not a matter for the state to interfere with".
Next week is the tenth anniversary of the London bombings in which Islamists killed 52 people and injured 700 more in an attack on the capital's transport system.
Blair, who ran London's police force at the time of the attack, said it would be a mistake for the government to be seen to be picking on British Muslims.
"Some people might argue we must take a much tougher approach but I couldn’t agree less with them," he said. "We have to take a very resolute approach, be resolute in actually requiring and demanding this community works with us, with the rest of us, with every creed and colour and gender across the UK to say, we must stop this happening. But you don’t do it to them, you do it with them."
He said: "It seems to me we have to accept there are people who live their lives by fundamentalist rules…Fundamentalism in itself is not a matter for the state to interfere with, it’s when it slides into violent extremism it is, and it’s that journey the Prime Minister and Secretary are trying to fix, where’s the point on that journey? But if we cut ourselves off from talking to some people whose views we do not like but to whom millions of young people listen that’s a very difficult issue for us."
"I just think we have to be incredibly careful, we shouldn’t be doing this to the community, we should be doing this with the community."
Blair added that he did not think he would live to see the end to Islamic extremism. “I’m 62, and I don’t think I’ll see it in my lifetime," he said.