Tommy Robinson denied claims his group had firebombed an Islamic community centre in London, where the letters EDL were sprayed on the building.
He admitted some of its tactics were "completely questionable", but said "working class people" had no choice.
The Muslim Women's Network UK said it had seen a rise in verbal abuse and intimidation since the Woolwich murder.
Mr Robinson was speaking after six men were jailed for planning to bomb an EDL rally in West Yorkshire.
The men, who all lived in or near Birmingham, were each jailed for more than 18 years. Their bomb plot failed because they arrived two hours after last year's rally in Dewsbury had finished.
'Completely questionable'
Mr Robinson told BBC Radio 4's Today programme he condemned all acts of violence by EDL members and the group was about peaceful protest.
He denied his group was behind the blaze in Muswell Hill last week and said the graffiti could have been placed there to make it look as if the group was responsible.
"If something was set fire and someone wrote David Cameron on the side of it, does it mean he did it?" he said. (+ BBC audi) » | Tuesday, June 11, 2013
BBC: EDL protest policing 'the price of democracy' » | Len Tingle | Political editor, Yorkshire | Monday, June 10, 2013
