Meths

A large proportion of people who vote for the BNP aren't actually racist. 

Although there are of course a fair few members and supporters motivated by racism, any near-mainstream support they have is from relatively normal people, usually among the white-working class. They vote for them because the government (not just the current one) has repeatedly failed to address some perfectly valid concerns, namely immigration and employment.

A complete halt to immigration is of course a bad idea, as is the probably-forcible removal of anyone described as not native (not exactly sure how many generations your family have to have been here for for you to be considered "native" but I suppose that's because it's actually skin colour and not nationality they care about). 

However, it is legitimate to question immigration and have some kind of discourse on the topic, something the government has flatly refused to do. Ever. Anyone bringing up the topic is usually called a racist and told to go away. 

The government has bred this problem and it is entirely of their own making. The only question really is why the government would do such a thing. Which option I choose generally depends on how cynical I'm feeling (veering between really, really cynical and merely really cynical)...

1)They don't care. The BNP will never be a real threat to any of the existing major parties. Nothing short of a nuclear holocaust (see what I did there?) would drive people to such extremism. Hopefully, we're a bit beyond a bit of a recession driving us into the hands of fascists. 

The main parties have been chasing the votes of the middle class ever since they started to emerge in real numbers after the war. The working class decreased in numbers and they tended to vote Labour anyway so they weren't seen as important enough to bother with. In a 2 party system where the only other "real" option was the Tories, enough of them weren't going to change voting habits and go for a minor party. Or they'd just not vote, in which case nobody really cared. Labour would have but they were making enough grounds with the richer sections of society that they didn't feel threatened by any loss of support, especially since it came in solidly Labour constituencies.

And if they needed any more incentive to not care, immigration results in what the government wants which is economic growth. Immigration is good for business and good for the economy, which is of course the ONLY thing the government really cares about. If a few poor people do lose their jobs or take a wage cut due to immigration, they don't care because businesses do better and the little numbers describing the economy increase. All of this means the government is more than willing for the BNP to get some support because the pay-off is worth it.

2)They want the BNP to have support. This, oddly enough, is the more cynical approach. How many people have told you to vote for someone in these last elections just so the BNP don't get a seat? They are an absolutely brilliant propaganda tool. In a system where people are routinely required to choose, not for who they want, but for who they despise less (the lesser of two evils), it is extremely handy if you have a bunch of racist fascists. Then you can just paint yourself as the lesser of two evils. Even more handy is that you don't even need to bother because people who admittedly mean well are but are actually absolute suckers will do it for you. I.e. all those people who told you to vote for anyone as long as it wasn't the BNP. 

The government has even less incentive to change when people will vote them anyway just to keep out the BNP.

They're probably both true, the second one just turned out to be an added bonus of the BNP. Unfortunately the fact that the BNP got seats at all is due to lower turnout which in turn is a result of the expenses scandal. This allows the government to portray it as a one-off and pretend it's only about one issue and not their abject failure for the past 40-odd years.