Well, the link says it might be EDL, unless they're the same organization.
They're not. The BNP are a political party (hence the "P") formed in 1982 as a National Front splinter group, who went on to achieve greater electoral success (especially during the New Labour years, 1997-2010), mainly due to slightly smarter marketing; namely, whilst the NF definitely sound and look like racists, the BNP is cunningly named as if in analogy to, say, the SNP (the Scottish Nationalist Party, who have never shown signs of official racism) and even more cunningly, they attempt to appeal to the non-racist vote by arguing that they're not racists.
The EDL is a protest group, formed initially from football hooligan subcultures, and are largely about protesting Islam (or, indeed,
the Muslamic Infidels), albeit with a strong undercurrent of racism.
The NF are still going, but are now as irrelevant as the 115,928 communist parties that also stand for election in the UK every general election.
For some reason, pretty much every visible organisation claiming to speak for Muslims in Britain turns out to have homophobic views, allegations of antisemitism hovering over them, or some other indication of being completely bonkers. It's not clear why this is, although if I had to guess, I'd say it's because for the
Daily Mail side of the press, it allows for easy generalisations to keep these guys in the spotlight, and the
Guardian side doesn't generally seem to have the spine to criticise.