freeriver I also stop and bow my head if there's a hearse passing - I live very close to an enormous cemetery, so it happens quite often! I've noticed, too, that most people round here do too.
My grandmother's aunt's funeral was in the town where she was living when she died, and she was taken back to be buried next to her husband the following day. On our way to the church, we saw a van pulled over, bring booked by the police. When we got to the church, we were all hanging around waiting for the coffin to arrive - it turned out that the van we saw being nicked was the hearse!
I would be very careful not to get in between the hearse and the funeral cars, but sometimes, there can be quite a long cortege of other vehicles following - in which case, sometimes you can end up overtaking etc completely by accident as, indeed, people have when I've been in funeral processions. I agree it's rude to cut up, overtake, or otherwise disrupt the main part of the procession, but sometimes, it's hard to know where to draw the line.
On another note - does anyone know if it's true that undertakers carry the cane in front of the hearse because of the days they would have had to beat off body snatchers?