My idea was that watching BBC would make things more clear by the fact that everything besides the logo is blurred.
That sounds just like the sort of stuff they come out with on W1A.
With regards to your mock, um, I don't get it. This is a blurred time-lapse shot of Big Ben and the House of Parliament with some slightly off off-centre writing on it. What are you trying to do? Either blur the entire background and put the writing on top of the blur or don't blur the background and have a legible set of characters instead. Trying to be clever and mixing the two just generates a frosted glass effect that in this case doesn't really work.