As far as I know, all Councils have a range of powers to deal with people or organisations causing a nuisance from a number of sources, eg litter, dust, noise etc.
They can make them clean up, change working practices or stop altogether - and be fined or even closed down, as necessary.
The fact that the operator of the recycling plant (who I assume are the culprits from what you say) just happen to be contractors to the Council shouldn't make any difference. Indeed, as they have got a contract with the Council, then the Council should be in a better bargaining position.
I think your first port of call is to contact the Council to -
a) Complain about the arrangements at the recycling plant,
b) Speak to the Dog Patrol department, and
c) Suggest that more litter facilities are provided.