Darlington Borough Council said some households had told the authority they did not regularly use the service because they generated very little food waste.
But the authority has urged residents to continue putting their food waste bins out every week, saying “every little helps” to reduce the amount of rubbish sent to landfill.
In a message to residents, the authority said: “Some of you have told us you produce very little food waste, so don’t regularly use the new weekly recycling collection service.
“Don’t forget, tea bags, coffee grounds, meat and fish bones, plate scrapings and peelings can all be recycled.
“Even if you have only a small amount of food recycling, please put your bin out for collection each week – every little helps divert waste from landfill.”
The borough-wide scheme began in June after new food waste bins, kitchen caddies and recycling bags were delivered to every household.
It forms part of a government drive to increase recycling rates and reduce waste contamination, with £1.5 million in government funding paying for specialist collection vehicles.
Earlier this month, the council’s cabinet member for services, Libby McCollom, urged residents already using the scheme to encourage others to take part.
“If you are already recycling your food waste, please encourage your family and friends to do the same,” she said.
“I would urge everyone to think about what they throw away, and whether or not it can be recycled to make something new rather than just heading to landfill.”
The introduction of the scheme means most households now have up to six bins for different types of waste and recycling.
Contamination stickers will be issued to households that place the wrong items in recycling bins, the council warned, after saying entire collection wagons can become contaminated by mixed waste.
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However, it has ruled out fining residents who fail to sort their waste correctly.
Ben Grabham, the council’s assistant director for environmental services and community safety, said the authority would focus on education rather than enforcement.
“We want people to recycle as much as possible, and we need to help them do that,” he said.