Just a quick sum up - this story has been told to me on a few occasions by my grandmother and it's her story. This does mean I know the story well and won't miss out on anything.
As a young girl my grandmother lived about a mile away from her school in a small town in East Anglia with her grandmother and 9 other relations. Every weekday morning she would have to cross a field with a friend and pass a small cottage before arriving in a more built up area where her school was located.
Passing the cottage every morning, she would be met my the elderly woman in her garden who had lived in the cottage for many years on her own hanging up washing or collecting water from her outside tap (taps used to be outside the house). As she passed by in the mornings they would always greet each other with a friendly hello as they had done for many years because it had become a habit.
One morning my grandmother was walking to school and as she had done the day before, greeted the old woman with a friendly "hello" before heading off to school. When she returned home that evening my great-grandmother told my gran how it was very upsetting that the elderly woman had died in her sleep that night and was found by a nearby neighbour. My gran told her mother that this was impossible, she had only seen her that morning.
My grandmother never saw the ghost again but is not frightened about the fact that she saw the old woman. Gran likes to think that it's was the elderly woman coming back to say goodbye, and takes comfort in this thought.