Prime Minister David Cameron says the country will be "resolute in the face of terrorism" after the brutal killing of a soldier in Woolwich, London.

"Good morning. What happened yesterday in Woolwich has sickened us all. On our televisions last night and in our newspapers this morning we have all seen images that are deeply shocking. The people who did this are trying to divide us. They should know, something like this will only bring us together and make us stronger.

"This country will be absolutely resolute in its stand against violent extremism and terror. We will never give in to terror, or terrorism in any of its forms. Second, this view is shared by every community in our country. This was not just an attack on Britain and on the British way of life; it was also a betrayal of Islam and of the Muslim communities who give so much to our country," he said.