As previously reported by The Herald, a small fire was seen burning on the pavement at the junction with Mitchell Street near Caffe Nero.
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A woman, 39, and 44-year-old man have ben arrested and charged in connection with the incident.
They are both due to appear at Glasgow Sheriff Court at a later date and a report will be submitted to the Procurator Fiscal.
Officers said there was no damage caused by the fire and there were no reports of any injuries.
A Police Scotland spokesperson said: “Around 6.45pm on Friday, August 22 police were called to a report of two people taking part in a demonstration and a fire outside on Gordon Street, Glasgow.
“No damaged was caused by the fire and there were no reports of any injuries.
“A 39-year-old woman and a 44-year-old man have been arrested and charged in connection.
“Both are due to appear at Glasgow Sheriff Court at a later date.
“A report will be submitted to the Procurator Fiscal.”