Far-right protesters marched through the streets of central London chanting anti-Muslim slogans as part of the backlash of the killing of a British soldier last week.

Anti-Islamic sentiment has been spreading through the UK after 25-year-old Lee Rigby was hacked to death in a south London street by two men claiming religious motivations for the murder.

About 1,000 protesters, spurred on by leaders of the far-right English Defence League, gathered in London shouting slogans such as "Muslim killers, off our streets."

In the tense, but largely peaceful demonstration, marchers rallied outside Prime Minister David Cameron's residence waving placards and shouting anti-Islamic obscenities.

"Islamic extremism is probably the number one threat to Britain," one protester, Ben Gates, said.

Since Rigby's death, mosques have been attacked and two men were arrested overnight on Sunday for throwing firebombs at an Islamic cultural centre in Grimsby, in the northeast of England.

'Very aggressive attacks'

Faith Matters, a charity working to defuse religious tensions, said it had registered a spike in reports of Islamophobic attacks in calls to its hotline, describing incidents as "very focused, very aggressive attacks".

Nearly 2,000 people marched at a similar demonstration in the northern city of Newcastle on Saturday.

As anti-racist groups warned there could be more reprisals, Cameron came under intense pressure on Monday for going on holiday, with pictures of him relaxing in Ibiza prompting newspapers to question his leadership at a time of unease.

Two war memorials in London were vandalised with red graffiti overnight, including the word "Islam" spray-painted onto one monument.

In an attempt to counter the right-wing rally, anti-fascist group Unite Against Racism held its own demonstration nearby but was heavily outnumbered by EDL protesters.

A handful of far-right demonstrators threw bottles and coins at the anti-fascist rally. Police vans and officers blocked the two groups from approaching each other.

"They are a minority and a very scary growing minority," an anti-EDL protester who gave her name as Clara said. "I feel ashamed to be a Londoner today. This is disgusting."