My two cents...
I have carefully re-read the BNP manifesto of 2005 and am unable to find evidence of Right-wing tendencies.
On the other hand, there is plenty of anti-capitalism, opposition to free trade, commitments to "use all non-destructive means to reduce income inequality", to institute worker ownership, to favour workers' co-operatives, to return parts of the railways to state ownership, to nationalise the Royal National Lifeboat Institution and to withdraw from Nato. That sounds pretty Left-wing to me.
Norman Tebbit must be either completely out of touch with reality or have become so gullible that he believes the BNP's pernicious propaganda. Of course it is an extreme Right-wing party. And Rachel Sylvester is right to describe them as such.
The BNP is strongly hostile to all minorities. It sells books which claim that black people are genetically inferior to whites. Its manifesto states that anyone who cannot prove a pre-1948 British heritage will be asked to leave. It is pretending to care about workers' rights to try to get the working-class vote - that is why it is targeting working-class areas in the local elections.
I have very little sympathy for Prentis's views here. Tebbit has specified economic and social policies that are explicitly left wing. Prentis has described the BNP as racist and therefore right wing. That is the only element he mentions. The problem here is that "right wing" has come to mean no more than "something of which I disapprove." If the terms are to have any meaning at all, it must by a socio-economic one. Chris has recommended that it be framed in terms of statist and non-statist, which seems reasonable, as well as choosing the interests of rich or poor, which seems a bit tendentious.
In any event, it seems clear that the old tribal differentiation no longer has any real meaning. This is largely because the old left wing has almost completely assimilated the old right's economic policies. It remains to be seen whether or not the new right will do the same with the left's social policies.