This system actually makes it HARDER for the BNP. The BNP managed to gain council seats with only getting 30% of the vote due the Conservatives, Labour and Liberal Democrat candidates all evenly split.
In the AV system, people can give their preference to the higher placed candidate in case their most preferred does poorly.
For example, if there are four candidates, your average Conservative might vote like this:
1 CON
2 LIB
3 LAB
4 BNP
in the same situation.
They don’t have to worry about helping a BNP candidate get elected because they know if the Conservative candidate comes last, their vote can be transferred to either the Liberal Democrats or Labour.