Axel's mother, Linda Peanberg King, told St Pancras Coroner's Court that she and her husband Alistair made contact with the Harmoni centre in the Whittington Hospital in Archway, after their son fell ill on the night of October 30 last year.
Five days later - after consulting at least three doctors - he died from bronchopneumonia.
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.