Religious groups and charities came together tonight to condemn the attack.
The Muslim Council of Britain said the killers’ use of “Islamic slogans” indicated they were motivated by their faith.
A statement from the council said: “This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family.
“We understand the victim is a serving member of the Armed Forces. Muslims have long served in this country’s Armed Forces, proudly and with honour.
“This attack on a member of the Armed Forces is dishonourable, and no cause justifies this murder.”
The group called for vigilance and solidarity between “all our communities, Muslim and non-Muslim”, and for police to “calm tensions”.
Akbar Khan from Building Bridges said: “We totally condemn the killing of an innocent person in Woolwich this afternoon.
“And we also condemn all forms of extremism wherever they are.
“The thoughts of the Muslim community are with the family of the man who lost his life, and we pray for him.”
Mohammed Shafiq from the Ramadhan Foundation said: “I wish to condemn the evil and barbaric crime carried out today in Woolwich.
“Our immediate thoughts are with the family and friends of the victims. From whatever angle you see today’s attack, it was at every level evil.
“We must allow the police to gather all the facts before unnecessary speculation and wait for the facts before determining its impact on our country.
“But what happens in the days to come, London and our nation will come together and will not be divided. The terrorists will never win and succeed in their evil plans.
“But tonight we think of the family of that soldier killed.”
Fiyaz Mughal, the director of charity Faith Matters, said: “The cold-blooded killing of a serving British soldier is a crime that sickens every member of every community in the UK.
“For the peace of our communities to be shattered like this is almost unthinkable. We must come together, isolate those who believe that extremism and violence are acceptable, and work to ensure that they meet the full force of the law.
“We must send a clear message to anyone that an attack on a serving soldier going about their daily activities is something that must be utterly condemned.”