The firm, which holds a 30-year contract to collect and process Sheffield’s rubbish, is paid £207,000 a year to provide assisted bin collections to more than 20,000 households where elderly and disabled people live.
Under the service, people who are unable to take their wheelie bins to the kerb themselves have them collected from beside their homes and then returned.
But the GMB trade union, which represents binmen, said that workers’ rounds are exactly the same regardless of how many assisted collections are on them and binmen themselves receive no extra payments.
It is not known how much Sheffield Council was charged for assisted collections at the beginning of its contract with Veolia, which was signed in 1999.
But if the current £207,000 annual bill was the same for all 30 years of the contract, the total cost to taxpayers would come to £6.21m.
Peter Davies, regional organiser for the GMB, which represents binmen in Sheffield, said: “The guys do the assisted collections as part and parcel of their work. They do not get extra payments, and the rounds are the same regardless of how many assisted collections there are.
“I do not understand how Veolia can justify charging the council the amount they do.”
A Veolia spokesman said: “Assisted collections are operated to households where the occupier is physically unable to present their waste containers for emptying.
“The council provides details of the locations which require an assisted collection, and the crews collect the full containers and return them to the same location after emptying.
“This system has operated throughout the 18 years that wheeled bins have operated in the city. The assisted collections form part of the overall workload of the crews and is reflected within their stabilised wages.”