Generally, I think "the bbc" is centre-left (upper-middle-class flavoured).
Their positions on most issues conform to that faction.
Their positions on most issues conform to that faction.
The reason I'd describe it this way is that it's much more apparent on social issues and certain aspects of international relations, where they don't even seem to understand that other viewpoints might exist. On economics they seem to have at least some awareness that there are a spectrum of viewpoints and take a more consumerist view as often as they do a soft left view (although they still never really seem to consider libertarian or harder left viewpoints).