Rubbish which was meant to be recycled has been piling up at a household waste site after collections were missed.
FCC Environment told South Hams District Council in Devon that 1,000 collections are being missed every day.
It blamed more waste than expected, creating a "bottleneck" at its processing plant.
Householder David Acklam said he got so fed up waiting for a collection he took the waste to the household waste site.
"When I got there I realised I'm not the only one. There are big bags full of plastic bottles and tins waiting to be recycled," he said.
"I couldn't leave it at home - there's so much of it and it will be spread by the seagulls.
"It's a ridiculous situation."
Some residents say they have been waiting six weeks for a collection.
The new scheme, which replaces plastic bags of recycling with reusable plastic boxes, was introduced in March.
At the launch the council said that it had been called "best in class" by "many other local authorities".
It changed a system of collections of paper, plastic and tins in plastic bags to one with plastic boxes for paper, cardboard and glass, another container for plastic containers and tins and another for food waste.
Martin Barfield, of FCC, told an extraordinary meeting of the council that the amount of waste, especially cardboard, was "way beyond" the amount predicted.
He said the company acknowledged that the service was unacceptable.
A "bottleneck" had been created at its Ivybridge processing plant because of the amount of waste, despite extra trucks and drivers being brought in.
"If you double the number of vehicles, the wait increases," he said.
The firm, which has 60 recycling contracts around the country, admitted that the current system was "unsustainable".
He said: "We are sorry to those residents that have not had the service they deserve.
"We are doing all we can to put it right."