Groups responsible for putting up flags told the BBC they are motivated by pride and patriotism, but the petition stated they made people “feel unwelcome in their own neighbourhoods”.
During the summer, Bristol council leader Tony Dyer said they would only be taken down if there were safety concerns, external, arguing it was time to “reclaim our flag” from those who had “hijacked” it for racist purposes and “reclaim the fact the flag represents all of us in England”.
But at the City Hall meeting on Friday Williams said: “The administration has discussed the situation many times and our position is an evolving one.
“It’s a dynamic situation. People should not be putting flags on public property, whether it’s lampposts or railings or roundabouts.”
He also explained the council had considered the safety of staff removing flags, as this had led to conflict in other parts of the country, with police or security staff to potentially flank workers where necessary.