Surrey Police say "the large fire" at Chessington will cause road closures for a "considerable amount of time".
Officers are asking drivers to avoid the A243 as well as the Chessington area.
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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.