Labour MP Hazel Blears says the Government has failed to to take action at local level to prevent the radicalisation of young Muslims.
The former counter-terrorism minister told BBC Radio 4's Today programme that she supported Prime Minister David Cameron's creation of a task force to crack down on extremism, but said the coalition Government had focused on policing and security measures rather than supporting integration.
"I actually think it's really important for young people in communities to feel that this is their community and that way you stop the next generation being groomed into extremism," she said. "I think the two things do have a connection."
She said banning extremist preachers' websites was not enough and that young people need to be empowered to say "this is not our religion, this is not our belief".
ITV News has uncovered a video showing Woolwich suspect Michael Adebolajo speaking at a demonstration at Harrow Central Mosque in 2009.
Documents suggest Security Services were trying to recruit Woolwich suspect Michael Adebolajo and had also approached members of his family.
Police in Kenya say they did everything they could to highlight their concerns about Michael Adebolajo.