Amber heat alerts are in place across the weekend, and into next week, for the Midlands, eastern and south-east England.
The prospect of comfortably beating the current record (32.8C) is "bonkers", according to BBC Weather's Simon King.
A huge column of black smoke was seen rising from the Clearway metal recycling facility in the city's Titanic quarter.
Eight areas in England, including Heathrow Airport and Kew Gardens, have met the threshold for a heatwave so far today, the Met Office tells the BBC.
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