Attacks on Muslims have also increased sharply since the murder.
Faith Matters, an organisation that works to reduce extremism, said more than 160 incidents had been reported to its helpline since the murder, compared with the average of four to eight cases a day before the attack.
Fiyaz Mughal from Faith Matters said there had been "a substantial spike" in reports of Islamophobia, from "general abuse [at] visible Muslims on the street to graffiti at mosques, through to a firebomb at a mosque". He added: "We're asking for cool and calm heads."
Another group, TellMamaUK, which supports victims of Islamophobia, reported a tenfold increase in reports of incidents over the past few days.
Social media sites were hosting dozens of offensive exchanges about "dirty muzzies" by, among others, EDL supporters and people claiming to be "English patriots". There have been a number of arrests over offensive comments.
The British National Party announced it would be holding a demonstration in Woolwich. Saturday's visit to the site of the murder by party leader Nick Griffin was criticised as provocative by Akbar Khan, chairman of the anti-racist and community organisation Building Bridges.
He said: "It is a provocative action. All Muslims have come out and condemned this act of violence. Given the serene and sad atmosphere prevailing in the country, because of this death, he is being very cynical and exploiting the raw nerves for his benefit."
BNP organiser Adam Walker said that a "line has been drawn in the sand and it signals the beginning of the civil war we have predicted for years".
- Observer