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 25-year-old, who plays former stormtrooper Finn in the third Star Wars triolgy, takes the lead role in the new production of Woyzeck.
This fierce feature film debut from London director William Oldroyd couldn’t be further from the Scottish play of its namesake.
A guarantee from City Hall to bankroll the annual £2-3m bill was a key planning condition imposed by Westminster and Lambeth councils.