There has been a small shift in the right direction with the emergence of new community groups and civil society initiatives, he said, but changes need to happen faster.
"We need to have a very strong counter-narrative to the ideas of al Qaeda," he said, which suggest that there is a war against Muslims led by non-Muslims.
"We need a civic identity, we need to make people understand that we are all British citizens, we are all part of this society. Whether you disagree with a particular issue or not, there are ways to voice your feelings, and killing a serviceman is not one of those."
There is apprehension across Britain, not just in London, in the face of demonstrations by groups like the far-right English Defence League, he said.
As each side gets more radical, it fuels the other, he said -- and that has consequences for the vast majority of people who do not share those opposing views.
"Ordinary people always get caught up in the crossfire of extremism," he said.