South Yorkshire Fire and Rescue Group Manager Andy Hayter told ITV News Calendar the Asos warehouse blaze near Barnsley was probably caused deliberately, though investigations are still ongoing.
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The violence began after a counter-protester allegedly doused a female rally organiser with pepper spray.
As temperatures climb through the day, the warmest spots are likely to be across western parts of Northern Ireland and western Scotland.
Boris Johnson and Amber Rudd have both criticised social media giants for failing to detect and remove extremist material online.