Australia's defence chief on Tuesday warned military personnel to avoid known trouble spots and be extra-vigilant to the possibility of copycat attacks after the grisly murder of a soldier in London.

General David Hurley wrote to all service members ordering them to adopt enhanced security, including what they reveal about themselves on social media, following the brutal killing on a busy street of Lee Rigby by two Islamists.

His death was followed by the stabbing of a soldier in France in a busy underground shopping and transport hub, although authorities have not yet established a link between the two cases.

"I need you to be alert, not alarmed," Hurley said in the letter.

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

He demanded that all defence personnel 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."

The Sydney Daily Telegraph reported that troops were separately warned to avoid a well-known firebrand Sydney jihadist, who has allegedly posted material inciting hatred against the defence forces in the past.

The man, who cannot be named following a magistrate's order, was arrested by counter-terrorism officers on Monday and charged with making threats against a Commonwealth public official. He was denied bail Tuesday.

Hurley's warning came as British police arrested a 10th person in connection with Rigby's murder near a barracks in Woolwich last week.

This includes the two prime suspects, Michael Adebolajo, 28, and Michael Adebowale, 22, who remain under armed guard in separate London hospitals after being shot by police at the murder scene.

The attack by two men spouting Islamist rhetoric has fuelled community tensions in Britain, with several mosques attacked in recent days and a charity reporting a surge in anti-Muslim incidents.