I know the BNP are bad, are there links between them and the EDL?
Many.
On an individual basis, many members are members of both groups (the BNP is a organised political party, the EDL more a street movement, so they arent mutually exclusive).
The BNP publicly distances itself from the EDL, but actually you need to do very little digging to find they overlap:
http://kirkunity.blogspot.com/2009/10/just-who-is-edl-leadership.html
Islamic extremism is a serious problem (if somewhat over played) in the UK, but racist thugs like the BNP/EDL, who even have links to more extreme UK neo-nazi groups like Combat 18 are NOT the answer.
Tight immigration, the end of PC-ism, and the end of the failed multicultural experiment and a return to a more homogenous British culture which can safely incorporate its different strands, be they Scottish, Irish, black, Muslim etc IS the answer.