It depends what kind of power you are talking about.
If you are talking about winning a general election, then I can't see this happening without a shift in the political paradigm, but with a shift, it could occur -- and the opportunity could be there over the next ten to fifteen years.
The danger would be that the BNP slowly increases its 'cultural power', as it has been doing over the last ten years, and the party begins to look viable as parts of the electorate begin to sympathise with some of its aims and policies. This growing viability then makes the party look like a possible channel into government for certain types of middle-class 'respectable' types, and they then join -- this has already started to happen in my view (BNP ballerina et al).
This then further 'normalises' what are essentially very radical policies and viewpoints, BUT the party also mutates at the same time -- you could call this the "Blairification process", where the old edges are filed down or appear to disappear all together.
What you then end up with is a weird hybrid that is highly 'electable', and would possibly then be elected to parliament and win a GE, but also has some old ideological baggage under the bonnet that ends up being played out as policy, but in a way you do not even notice.
You end up with a Janus-faced government.
This is the path that I feel the BNP could go, which makes me state I don't think the idea of gaining power is overhyped -- they already have far, far more sympathetic and cultural power than they had fifteen years ago.
To my mind, a rather good idea that I read elsewhere this morning would be for the two main parties to split into four, and stop shoehorning such a wide spectrum of opinions into 'Tory' and 'Labour'. This could go someway to retaining disaffected working persons' Labour votes within the traditional paradigm, as a distinct voice apart from the elitist liberal Labour block, who can afford to be more ideological.
Same would go for the Tories. You'd stop the "Tories are going soft with a Blairite Cameron" mantra if they had somewhere to go that was "parochial Conservative" -- Ukip did this to some extent, but they still suffered from new party syndrome.
Any new political party has to build up years of awareness and viability, tried and tested methods of decision-making etc, a way to hang together without silly tenuous splits.
And I don't think there is time for a new party to do this and thus soak up disaffection.
Mibbe.