If the remittance did not have any "reference" details, I am not sure
what either your or the client's bank could do to help and even if the could, I guess it may have been a case of "I know, I will use the DPA to avoid doing any work to find out?"
Looks like this is something you will need to address direct with the clients or their own account departments?
A customer of ours invariably made payments without quoting any details. After several months, our accounts department got fed up of the behaviour so I shredded the next cheque received and issued an overdue account notice. We never had any problems after that.