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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The high of 35C was recorded on a Bakerloo line train between Piccadilly Circus and Oxford Circus at 2pm.
Weather forecasters say temperatures could reach 35C, beating the previous record of 34.6C in the scorching summer of 1976.
After years of political manoeuvring over the future expansion of Heathrow Airport, there has been an important development this lunchtime.