The motion to remove the fee failed.
Glasgow’s conservative group brought the issue, which also called for tougher penalties on those caught fly tipping, before the full council meeting last week.
The group also attempted to move a vote of no confidence in the council leader as part of their motion but Lord Provost Philip Braat would not allow this to go ahead as the call came too late in the day.
Labour and the Greens instead moved a joint amendment to instruct councillor Susan Aitken to respond positively to the GMB’s requests, meet with them and front line staff prior to the next full council meeting and discuss proposals and solutions to the cleansing crisis.
The amendment which was subsequently agreed via a majority vote, 73-7, also states that Glasgow and Scotland requires legislative change to deal with fly tipping and that an urgent review is required to see how the local authority delivers its enforcement work.
The review will also look into changing bulk uplift charges in the future with a report brought back to the next environment committee.
Conservative councillor Euan Blockley said he was angry at this amendment and said that he was happy to condemn those who dump their rubbish illegally.
He said: “We are being told that other local authorities charge for bulk uplifts which they do but other local authority areas don’t look like Glasgow which is an embarrassment.
“The city is a midden and if you honestly think that putting a £35 charge is going to make things better you are delusional.
“What I can’t understand is that opposition members say they hate the charge and three weekly bin collections but when push comes to shove it’s all warm words – there is no action. You’re right, I am angry that my party is angry at the state of the city.
“The administration should be angry at this too. I’m furious at the fly tipping going on outside my door, potholes and the three weekly bin collections and complaints coming through to me.”
During the meeting Glasgow’s Green group criticised the implementation of the charging system, which they say was ‘railroaded’ through without oversight from councillors.
They highlighted issues with garden waste from tenement back courts, dumping in private lanes and shared back courts, and difficulties for those with no access to a vehicle.
The Greens also proposed periodic bulk waste ‘amnesties’ as another way to mitigate the impact of new charges, and called for steps to increase the reuse and recycling of items commonly presented as bulk waste.
Following the meeting councillor Jon Molyneux said: “No one should deny the impact of dumped waste on Glasgow’s neighbourhoods and poorly implemented changes to the bulk waste service do risk making a bad situation worse.
“That’s why we argued for a review of how bulk waste charges have been introduced, particularly so they take account of specific challenges some people have because of their income, their housing situation, or lack of access to a vehicle.
“While others play politics and make personal attacks, Scottish Greens will keep working to improve local services.”