A councillor said more than 1,000 residents have signed his petition opposing a plan to introduce fortnightly bin collections.
Havering Council included a proposal on changes to how it collects rubbish in the borough as part of its 2023/24 budget plans.
The authority wants to move to alternate weekly collections, where it picks up recycling one week and other household waste the next week.
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But Conservative councillor David Taylor, who represents St Edwards ward in Romford, is opposing the move.
His petition calls on the council to retain weekly collections.
He said: "Many of my residents live in flats, or homes, with nowhere to store rubbish for two weeks.”
Havering Council did not respond to a request for comment.
The council said in its budget consultation document that the plans to change collections would save it around £650,000 a year.
The authority is also planning to increase garden waste charges and bulky waste collection charges, which it says could raise an extra £285,000 income over four years.
It adds that it will provide most households with wheelie bins.
The proposed changes to waste collection comes with the council looking to plug a £70million budget gap.
Other savings plans the authority is consulting on include increasing council tax, which it says could raise up to £4.2m, and permanently closing Chippenham Road, Elm Park and Hilldene Children’s Centres.
The latter could save £1.6m over four years, according to the council.
In the budget consultation document, council leader Ray Morgon said: "This budget consultation makes proposals to save money that I know will have an impact right across our borough and may not be popular.
"If we cannot meet the challenges and make radical proposals for change, the council’s financial position will become unsustainable."
Cllr Taylor said his petition is set to be handed in at the full council meeting on November 23.
To sign it, visit www.davidtaylor.online/petition.
The council's budget consultation runs until December 30. To view the plans and complete the survey, go to consultation.havering.gov.uk/corporate/budget-2023/.
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