Australian Defence Force personnel have been warned to be on the alert for copycat attacks following the gruesome murder of a British soldier on a London street last week.

Drummer Lee Rigby was hacked to death by two men as he walked near an army barracks in Woolwich, south-east London.

His alleged attackers urged bystanders to film them in an Islamist tirade before being shot by police who arrived at the scene.

French police are investigating a similar attack in Paris, where a soldier was stabbed in the neck as he patrolled the La Défense business district.

Now Defence Force Chief David Hurley has written to all military personnel to warn them about the "possibility of further copycat attacks" on Australian soil.

"I need you to be alert, not alarmed," he wrote.

"Although there is no evidence of similar threats to ADF or Defence personnel, there is the possibility of further copycat attacks.

"All Defence personnel are to ensure that they exercise enhanced personnel security awareness and vigilance, particularly when off base and in uniform.

"You should exercise sensible security precautions, such as avoiding known or likely trouble spots, and take extra care in what you reveal about yourself and your planned activities in social media."

While there is no change in the overall threat level, General Hurley asked that each base review their security arrangements.

Overnight, , as demonstrators from the far-right English Defence League massed near Downing Street to vent their anger about the attack which has increased tensions in the UK.

Rigby's suspected killers, Michael Adebolajo, 28, and Michael Adebowale, 22, remain under armed guard in separate London hospitals after being shot by police at the murder scene.

Security committee discusses domestic implications

Prime Minister Julia Gillard has told Parliament that the National Security Committee of Federal Cabinet, the Government's most powerful security body, has considered the incident, which she described as an "horrific attack".

"I think members across the House would acknowledge, as I most certainly do, that that is some of the most disturbing images that I've ever seen, some of the most disturbing footage that I've ever seen," she said.

While emphasising that Australia's alert level remained unchanged at medium, Ms Gillard noted General Hurley's call for enhanced security awareness and vigilance.

"An incident like this emphasises the ongoing preventative work of federal and state agencies in countering similar terrorism threats to Australia," she said.

"The continuing threat of terrorism always has the capacity to shock and surprise us."