In the UK, car drivers are very bad at passing cyclists. For some reason they think we are happy to have just a few inches of space. They forget that we're balancing, and that we often need to swerve to avoid potholes. It's also an unfortunate happening that car wing mirrors are at roughly the same height as a cyclist's elbow...
Luckily being hit from behind is a rare occurrance for a cyclist, so while there is a strong perception that there is danger in reality this is not the case. With experience the fear of being hit by passing cars is dulled a little, but it never goes away.
Cycling assertively helps a great deal here. The worst possible thing to do is ride close to the kerb. Not only will cars pass you faster and closer, but if your front wheel hits the kerb you fall off. As a rough guide, aim to ride where the cars' left-hand wheels have made the road smooth and clean. You'll be more visible to drivers and you'll get a lot fewer punctures.