There are several possible approaches to this.
One would be for the council to stick to its guns. Assuming the arrangement is to pay for work actually done, and not a standard payment, then the council is within its rights to challenge whether invoice items are for work actually done. Debt collectors can do no more than bluster without a court decision. If the contractor went to the county court, the council could defend itself. The outcome of the court case would be binding.
However, it could be felt that the "aggressive" route involved too much potential for aggravation and wasted time. It could also involve additional costs. An alternative is to pay the invoice and terminate the contract. An informal discussion with the contractor prior to this action could raise the question of whether the contractor could find a way to resolve the issue so as to avoid losing the contract.
Yet another possibility would be to accept that if nobody can tell the difference, maybe the work does not need to be done. Or perhaps a fixed price could be agreed for the cleaning, with payment depending on the cleanliness of the areas rather than the hours of work done.