I was always under the impression that the licence was for the tuner, rather than the actual TV screen. I know that you used to have to get a colour licence if you owned a VCR, because it had a tuner capable of receiving and recording pictures in colour.
Now that we've gone through digital switchover, there are no purely B&W TV tuners - every digital set-top box can receive colour pictures, even if the TV can't display them.
Surely, in this case, the Black and White licence is obsolete?
(Incidentally, I dropped my TV licence this year - I just wasn't using it enough to justify the cost. What little TV I view now is on-demand through the computer. With fibre-optic broadband - paid for with the money saved by not having a TV licence - I can receive an HD picture on BBC iPlayer and it's actually better than the old TV reception.)