Greater Manchester Fire and Rescue Service are using a tactic to let the fire burn out in a controlled way.
Andrew Heywood told ITV Granada Reports: "It's large quantities of flammable material, paper, plastic that's been shredded and compacted...So there is a massive fireload in that building and it will continue to burn for days".
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Businesses in Chester are staying open later on Thursdays throughout the summer to encourage people to shop and eat out after work.
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