I would be asking your care centre to provide reference to the relevant legislation that has prompted their decision - because to my knowledge it is not legal for a centre to refuse to use cloth.

I believe CCCs have a dispensation from any Council requirements to dispose of solid waste in the toilet, for contamination/excessive handling reasons (change & nappy disposal areas are not always immediately convenient to toilet facilities, which are part of the accessible area of the facility, as they have to be separate from the areas accessible to children, so if the carer has to travel through the accessible area in order to dispose of waste this presents a contamination risk).

So long as their handling of cloth is consistent with their handling of sposies, which it is if they roll the nappy up without disposing of waste, deposit in a sealable container consistent with that used for sposies which is removed by the parent at the end of the day for cleaning - they have no legal grounds for refusing to use cloth.