More than 6,560 people signed a petition calling for the council to stop using glyphosate, which they say is a danger to health and damages biodiversity.
Last year 1,750 litres of the chemical was used on the city’s pavements, verges and parks.
Because the petition had more than 5,000 names, it automatically triggered a debate at a full council meeting held this week.
The petition was presented by Graham Wroe while the drama group Act Now performed outside the meeting with people dressed as insects and a globe.
Mr Wroe said: “Glyphosate contributes to the massive decline in the insect population which is not just bad for insects but every living thing on the planet as we rely on them to pollinate our crops. Glyphosate harms worms, the soil, trees, birds and animals.
“The World Health Organisation found it is probably carcinogenic. Employees should stop using glyphosate immediately and replace it with safer alternatives, many of which have been trialled by councils in the UK.
“The council spends lots of money spraying glyphosate to keep the city tidy, but much of it actually makes our city look less attractive.
“Verges often have a dead stripe along the edge, road name signs are surrounded by long dead grass, street trees are found in islands of poisoned soft soil where nothing can grow and pavement borders are full of rotting plants instead of pretty wild flowers.”
There was a complex discussion about how the council should proceed and eventually the Liberal Democrats and Greens voted that Coun Alison Teal would take the lead and the Executive would make a final decision.
Coun Teal, Executive member for neighbourhoods, wellbeing, parks and leisure, said: “A number of councils have already banned, rapidly phased out or placed restrictions on the use of glyphosate so this is nothing radical.
“We need to look at the full spectrum of the chemicals that we’re using at the moment, and I’m really pleased to hear that workers at parks and countryside are already trialling alternatives.”