Bike boxes at traffic lights - a little eye witness example

I've been sat for 30 minutes at a café on the corner of Great Smith Street / Great Peter Street in Westminster. This is the view of the cycle box on Great Peter Street, going westbound.

More than half of the times the lights were red cars stopped more or less completely in the cycle box. More than half the black cabs, to my surprise, broadly respected the cycle box. I wonder how many drivers actually know they are breaking the law though? Will £60 fines help?