BNP stands for British National Party by the way. Why do you love the word 'nazi' so much? Oh wait i see... When someone's not agree with you or you lose a discussion you just call him a nazi as argument? Thats clever
The BNP repeats and believes Nazi propaganda about Jews, for accuracy's sake. Many of the BNP members espouse Nazi-style Jew hatred. Calling them Nazis is short-hand.
And for the EDL, I completely understand that you'd take offense at them being called Nazis. Tommy was pretty much, so I don't understand why you're defending him, but if anyone says that the EDL is a Nazi organization, they're wrong.
As for Roberta Moore, her story shows that something is wrong. Would we kick you or a Hindu out for being another nationality/religion? Why does a counter-jihad movement push someone out who's counter-jihad? It's a fact that there are Jew-haters in the EDL, and while it's great B"H that you're not one of them, and that many aren't, they do wield a considerable amount of influence in it.
Do I wish EDL would succeed? Of course. However in Jewish tradition, people get kicked out of a G-dly army for insignificant sins that they could just fix later, because (more than just this) you want to make sure G-d is fighting with you. Unless everyone in the EDL hates Jews, they're divided against themselves, and all I have to say is identify the enemy, and put your will to survive above your petty conspiracies and ignorant prejudices. Serbia did it, and would have been fine if not for us, but they continue to survive. Finally, take everything that you hear from the EDL with a grain of salt. They're still highly politically correct based on the statements I hear, and I never trust people themselves or to accomplish much who water down their message to win.