You may cross the line if necessary, provided the road is clear, to pass a stationary vehicle, or overtake a pedal cycle, horse or road maintenance vehicle, if they are travelling at 10 mph (16 km/h) or less.
I can see the driver's argument being that as you are riding a pedal cycle either you were in the wrong for doing more than 10mph or the speed difference between 16 and 60mph is such that the driver thought you were doing 10mph.
Probably the latter. Most of the time drivers tend to treat cyclists as if we're doing little more the walking speed, even when we're really not. I suspect it's because the difference in closing speed is negligable, and it's hard to determine the speed of a two-wheeler by looming at the best of times.
Indeed, when I'm driving, I tend to use cyclist knowledge to help guestmate the speed of distant cyclists (pedalling cadence, type of bike, clothing, road positioning, gradient and quality of road surface, etc.), which you can't reasonably expect most drivers to be able to do.
The law isn't really working, but I can't think of a sensible alternative. There are always going to be circumstances where it's reasonable for driver to cross solid lines to overtake something slow.