You know that many of these 'nazis' maybe Agent Provocateurs' the police hired to make the EDL look bad it's done often.I know in the U.S. they say at any Klan gathering half the people there are FBI agents. For another example take C18
Searchlight, Red Action, and other commentators on both the left and right, including journalist Larry O'Hara, have speculated that C18 was created by the British internal security service MI5 to discredit the BNP while acting as a honey trap, or sting operation, designed to attract the most violent neo-Nazis in the UK into a single organization, where they could be monitored more easily. Some commentators also suggest that it was used by MI5 to infiltrate Loyalist paramilitary groups in Northern Ireland.
In 1998, the leader of C18, Charlie Sargent, an alleged Special Branch informant, was sentenced to life imprisonment for the 1997 murder of another member of the group so you see many of the supposed 'Nazis in the EDL may very well be agents of the left or the Police