I drive too (as most of us do) - personally, I'd have stayed behind (given the situation you've described), and that's the course of action I'd recommend (again, based on what you're described).
As would I have, eased off the speed as soon as the cyclist was spotted and control the situation with speed or lack of speed and coast up behind the cyclist, and thereby minimising angry drivers because I imagine sharp braking produced the upset behind when the under-take wasn't possible.