The two groups therefore held static protests in different areas of the city.
Pressure and tension
EDL supporters demonstrated at the Urban Gardens area of the city centre, while between 250 and 300 Unite Against Fascism supporters rallied at the Crown Court plaza.
Another 150 people attended an event called Be Bradford – Peaceful Together, at a separate part of the city, Infirmary Fields.
But EDL supporters threw bottles and stones and a smoke bomb over a barrier temporarily erected to separate the two groups.
They were later moved from the area by security forces.
Al Jazeera's Paul Brennan, in Bradford, said: "There is a huge amount of pressure and tension in this city today.
"Not least because of the echoes of the 2001 race riots. They have left a lasting scar on this city and there was a real expectation that today might be a repeat of those riots."
'Opposing the Taliban'
Analysts have drawn connections between the EDL, which was formed about 18 months ago, and the British National Party.
The EDL deny this and accusations that the group is racist or fascist. Rather it has said that it is simply against the Taliban and extreme forms of Islam.
"Frankly, you can take that with a pinch of salt," Brennan said.
"Because the evidence is in what they do rather than what they say. And what they do is certainly very indicative of a far-right organisation which has much wider political aims than simply extreme Islam," he said.
Bradford is about 78 per cent white and 12 per cent ethnic minorities, predominately Pakistani. However, in some areas of the city the Pakistani population make up more than 60 per cent of inhabitants.
About 190 people were given sentences after the 2001 riots.