Sue's point about the BBC's willingness to use the 'far-right' label is borne out by a simple search of the BBC website.
A search using the term 'far-right' brings up 2,651 news results, whereas an equivalent search using the term 'far-left' brings up a mere 211 results (over twelve times more often).
As with any other media organisation, it is the BBC's own choice - shall we say 'whim'? - to describe various organisations and parties in certain ways.
For example, it's long been their preference to label the kinds of protesters campaigning against the G8 summit as 'anti-capitalist' rather than 'far-left'. Those protesters are overwhelmingly anti-capitalist of course, so 'fair enough' you might say. They could, however, also just as accurately be described as 'far-left' - if you wanted to do so.
If the BBC (institutionally-speaking) were to develop an instinctive distaste for those anti-capitalist protesters I think it's highly likely that the corporation would begin referring to them as 'far-left G8 protesters'. I sense no such instinctive distaste.
The BBC (institutionally-speaking) does seem to have an instinctive distaste for the EDL though and their widespread use of the label 'far-right' to describe them seems rather more akin to an 'Urrghh!' than to a factual description. The term 'anti-Islam' would surely be a more accurate way to describe the EDL than 'far-right', wouldn't it?
Maybe media organisations should use such all labels much more sparingly.
You say 'potato'. I say 'left-far extremist'. Let's call the whole thing off.