Remaining household waste is set to be collected this week, after bin collections in Uttlesford were suspended due to an 'operational failing'.
Residents were left with their bins overflowing after Uttlesford District Council's transport manager left, and the licence was not renewed before their replacement was up and running.
One resident of Ongar Road, Dunmow, said: "We pay our monthly council tax. Our rubbish hasn't been collected for four weeks.
"I asked if we were going to get any gesture of goodwill on our council tax. They said 'no, we can't do that, it's set'.
"They're supposed to be providing a service for a fee and they're not providing that service.
"The licence not being renewed is not our problem. We shouldn't suffer because of that."
Another resident also complained about rats congregating around the overflowing bins.
Cllr Neil Reeve, the council's portfolio holder for the environment and climate change, apologised to affected residents for the "unacceptable" error.
Last week, on Wednesday, February 7, Uttlesford District Council announced that it would resume waste collections that day, after the Office of the Traffic Commissioner granted an interim operators' licence.
A statement from the district council said: "We fully appreciate how frustrated and upset residents are by the disruption and we apologise again for this breakdown of waste collection over the last couple of weeks.
"Our regular crews and vehicles are back out this week and we are aiming to visit all parts of the district on their normal days, although collections will be a little slower than usual due to the extra recycling that will be left out for collection."
The council explained that they would not be able to refund council tax due to the disruption, as the funding for waste collection services also comes from government grants and business rates.
Only around 8p in every £1 in council tax collected goes to the district council - with the other 92 per cent going to Essex County Council, the police, the fire service and parish or town councils.
On average, a week of waste collection services therefore costs each household 50p.
To help the council get on top of the backlog, other operators have stepped in to assist - including Widdington Recycling and Braintree District Council's in-house waste crews.
In an update today (Tuesday, February 13), a council spokesperson said: "Our vehicles and crews have been out today, supported by other trucks and staff from Braintree, emptying recycling bins and food waste caddies.
"We are aiming to visit all parts of the district on their normal days this week.
"The crews are making good progress but please bear with us - collections may be a little slower than usual due to the extra recycling that has been left out for collection.
"If necessary, we will send out crews on Saturday and Monday to complete the recycling collections.
"We are aware that some areas have not yet had their non-recycling bins emptied. We are sending out teams this week to complete the non-recycling collections."
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