Katy Skerrett, senior coroner for Gloucestershire, reached a conclusion of accidental death and said Dame Jilly, 88, died as a result of a traumatic subdural haematoma.
Ms Skerrett said Dame Jilly had been unable to give an account of what had happened, but it was believed she had fallen down a flight of stairs "as there was a trail of blood" in that area of her home.
An urgent CT scan revealed she had sustained a skull fracture.
"The medical opinion was that this head injury was unfortunately catastrophic and therefore likely a terminal event," Ms Skerrett added.
"She was made comfortable, her condition sadly thereafter deteriorated and she passed away in the emergency department with family present."
In a statement, South Western Ambulance Service confirmed it had been called at 5.35 BST on 4 October and arrived at Dame Jilly's home about 20 minutes later.
Ms Skerrett said: "The patient was able to speak to crew on arrival.
"She had no direct recollection of events prior. She was unsure how she had fallen. She had a vague recollection of falling down."