Eyewitnesses said the victim, who a local MP said was believed to be a soldier, was hacked to death, with some suggesting his attackers tried to behead him. Unconfirmed reports said they also filmed the attack.
UK Home Secretary Theresa May said: "I have been briefed by the Metropolitan Police Commissioner and the Director General of the Security Service.
"It has been confirmed to me that a man has been brutally murdered this afternoon in South East London. Two other men were shot by armed police and they are currently receiving treatment for their injuries.
Live coverage from the BBC here.