Tilly, big hug.
IME, a post mortem and inquest has only been held when the person has died unexpectedly. If the person has been under the care of a doctor in the previous couple of weeks (which your relative had), then (usually) the cause of death is known from the notes (e.g. if it had been something anticipated). My parents were the same - my dad was due to be readmitted on the following morning, he died before he got there - but they knew what he'd got, so no need to investigate further. "Natural Causes" sounds to be if it was just the end of their time in this life.