Last Friday, (August 1), Sita UK took control of waste collection across Calderdale meaning as well as picking up refuse the firm is responsible for collecting recyclables from all 90,000 homes.
But Sita has yet to distribute green boxes for cans, glass and textiles and green bags for paper to 25,000 properties including homes in Hebden Bridge, Mytholmroyd, Todmorden and other areas across Calderdale.
Instead it has asked residents to use "any suitable bag and bags" and leave them on the kerb.
But Kerbside Calderdale has pledged to continue collecting its black recycling boxes, giving householders a choice of which to use and commencing the competition.
Now in the first week of the dual collections Kerbside claim Sita has been taking materials left out for them but Sita denies the allegation.
The main problem is with items left out for collection in plastic bags, which don't have the logo of either firm on them, as Sita requested people leave their recyclables in this way but Kerbside say they always advised people to leave excess recyclables in a suitable bag by their black box.
Kerbside chief executive Paul Brannigan said: "There is no doubt that staff working for Sita UK have been taking recyclables that have been left out for us.
"People who fill our collection boxes are not going to put out a bag for Sita as well - we have always collected their bags if there was not enough room in the box."
There had been talks to try to prevent the battlelines been drawn by pulling the two organisations together.
Sita had offered to expand Kerbside's rounds to all homes and employ all its workers on enhanced pay, costing them an extra £100,000 a year, but that and other offers were rejected.
A Sita spokeswoman said: "Our workers were instructed to take any material left on the kerbside in carrier bags but that Kerbside Calderdale boxes were not to be touched.
"Householders should be receiving green Sita recycling boxes in the next couple of weeks and a leaflet explaining how to use them."