Jim Myers, 43, a door supervisor in the city, sparked controversy by saying Britain needed to follow the French lead and ban the burka.
But he has decided to stand down after last weekend's protest over a planned £18million mosque which left the people of Dudley, West Midlands, with a damage bill for £150,000.
Mr Myers, who lives in St Thomas, had, along with 13 other Exeter EDL members, taken a minibus from Cowick Street to join about 600 EDL protesters from across the country.
They were corralled in a car park but a group of about 200 protesters broke through the gates and clashed with lines of police and vans.
Bricks and cans were thrown at officers, forcing them to change into riot gear, and police dogs were brought in as a back-up. After a ten-minute stand-off with police, the protesters returned to the car park.
Houses and cars were damaged, missiles were hurled at officers and steel fences were pulled down.
Mr Myers, who, along with the Exeter contingent, was not involved in any of the disorder, said: "I was left really disgusted by what I saw in Dudley — from both sides, police and a minority of the protesters.
"There are always troublemakers who will latch on to a protest, whatever it is, and some tempers got heated.
"After what happened, I have decided to resign as Exeter chairman. We will have a meeting in August to see where we go from here."
Mr Myers also revealed that his hopes of holding a 9/11 memorial march through Exeter on September 11 had been dropped.
"I have spoken to the police, with whom I have a good relationship, and I have been told they would oppose such a march," he said. "We had hoped to remember those killed in the 9/11 tragedy."
He also indicated that he would not support a protest at the city's York Road mosque, which he admitted was being considered by EDL members.
The Muslim community in Exeter is said to be frightened at talk that the group — which has seen several of its demonstrations across the country end in violence — would target the mosque in York Road.
Formed just over a year ago, the EDL claims to be against "Islamic fundamentalists" but its opponents said targeting a mosque with no recognised link to terrorism was proof of the group's overall anti-Muslim agenda.
A South West division member says in a posting on the group's Facebook site: "I think a protest is due in Exeter at the mosque."
He then incorrectly states: "The council have given £3million to refurbish it and extremists use this mosque as it's out of the public eye.
"Exeter has had an attempted bomb attack and we don't want another. So please let's make this happen."
In fact, the mosque relies on public donations and the bomber who targeted the Giraffe restaurant in Exeter, Nicky Reilly, was influenced by extremists in Plymouth.
Lizi Allnatt, of the Exeter division of the Unite Against Fascism group, said: "Why have a demonstration at the mosque? It is like a church and is not a place that fundamentalists go to use. It is for everyday, ordinary Muslims. The Muslim community is quite rightly frightened at such a prospect."