The BBC expose, released in advance to other media, may also lead to criminal prosecutions.
In secretly recorded footage in the northern town of Keighley, BNP leader Nick Griffin - who recently hosted French National Front leader Jean-Marie Le Pen - rails against the Quran and acknowledges his views are legally dangerous.
"That's the way that this wicked, vicious faith has expanded through a handful of cranky lunatics about 1,300 years ago until it's now sweeping country after country," he says at one point.
He tells his audience they should stand up for the party or "they (Muslims) will do for someone in your family".
"For saying that, I tell you, I will get seven years if I said that outside," he adds.
Other footage in "The Secret Agent" shows one BNP member expressing a wish to blow up mosques with a rocket launcher and to machine-gun worshippers with "about a million bullets".
Le Pen was recently hosted by
BNP leader Nick Griffin
Another member tells how he put dog faeces through an Asian shop's letterbox, while a third describes how he beat up a Muslim man. "I'm kicking away ... It was fantastic," he says.
Police in the West Yorkshire region where filming took place said they were waiting for a copy of the programme to decide whether to press charges. "We will always prosecute where we find evidence of anyone being involved in racially motivated crime," a spokesman said.
Leaders of Britain's nearly two million Muslims - already worried about a rise in race hate since the September 11 attacks - said the programme unmasked the BNP.
"It has tried for a false image of respectability. Yet under the surface lurks the same hatred of the foreigner," Inayat Bunglawala, of the Muslim Council of Britain, said.
"The old-style racism of the BNP is now morphing into a more focussed anti-Muslim sentiment which is often now manifesting itself in outright acts of violence," he added.
The BNP's anti-immigration stance has won it a handful of council seats, mainly in poorer areas with large ethnic populations. But it remains on the fringe of politics and is largely ostracised by media and mainstream parties.
The BNP responded to the expose by expelling the two members who admitted assaults and vowing to discipline the third.
"The use of agents provocateurs is one of the nastiest hallmarks of a totalitarian state and the BBC is the propaganda wing of the Blair government's liberal totalitarian state"
Griffin said his comments were selectively edited to put him in a bad light and challenged authorities to prosecute him.
"If (Home Secretary David) Blunkett wants to put me on a show trial about whether we're entitled to warn about the dangers of Islam, I will be absolutely delighted," he said.
"The use of agents provocateurs is one of the nastiest hallmarks of a totalitarian state and the BBC is the propaganda wing of the Blair government's liberal totalitarian state."
BNP spokesman Phil Edwards added that most members were respectable members of the community. "You can't judge a political party by two or three yobbos," he said.
BBC reporter Jason Gwynne obtained his material over six months after infiltrating the BNP with the help of a former local leader who became a mole on behalf of a campaign group.