What if there is no GBH intent either? What if you are just being negligent or careless, like speeding while driving thinking you are a better-than-average driver and won't crash, or if you are not speeding and someone runs out in front of you, or if you are throwing roof tiles off a roof as you remove them while thinking people will see and hear what you are doing and walk around the pile, and you end up killing someone?

The death is evidence that you killed somebody, but you can still be "innocent of murder" (and guilty of manslaughter instead. In the UK). That's why there are so many varieties of manslaughter, to determine how culpable the person is, whether they were negligent, whether they were comitting another crime, etc.