Two groups of protesters needed to be separated as tempers flared in King Cross, Halifax.
EDL followers entered the park opposite the William IV pub, where an opposition demonstration, Unite Against Fascism, was taking place.
The EDL arrived by bus and began to taunt the UAF group by chanting songs.
The two groups had to be pulled apart by council officials before police arrived to separate them.
They were able to move the EDL on towards Halifax centre and police remained at the scene to allow the UAF demonstration to continue.
In the skirmish, a 21-year-old man was arrested for possessing an offensive weapon.
Several groups of EDL members arrived in Sowerby Bridge by train and walked towards the main demo in Halifax.
Around 30 members marched down the middle of road in Wharf Street, chanting and parading EDL banners.
Superintendent Stan Bates, head of operations for Calderdale Police, said: “The town was prepared to facilitate a peaceful protest.
“But many chose to cause disruption for a short time.
“Officers were at the scene in the King Cross area where there was a confrontation but nobody was injured.”