Scotland Yard said they were treating the toddler's death as non-suspicious and that a post-mortem examination was due to take place to establish how the little girl died.
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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.