Under the Clean Air Act 1993, it is an offence to cause or permit emissions of 'dark smoke' from industrial or trade premises (includes building & demolition). Burning can be deemed to have taken place (without witnessing a bonfire) if the materials that have been burnt on the premises are likely to give rise to dark smoke, e.g. cable, paint, etc. Cable burning is also a specific offence unless authorised.
The Clean Air Act 1993 also enables local authorities to declare any part of their district as a Smoke Control Area.
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