Have you been charged extra for the cremation?
Well, you can ask them to investigate. The truth will be that the answer will be there was some form of mistake.
The question is what is their liability. Clearly they should and they are refunding you for the charge.
There is probably no claim for additional compensation. The loss is an emotional one rather than anything that can be compensated by money. The actual money value of the lost ashes will be nothing like the emotional loss.
Can I clarify anything for you?
Not really. There is no overall regulator of the two.
The only way to regulate is to sue and since there isn't really a claim beyond the sums paid that is fairly difficult.
I cannot imagine trading standards would be interested. It is just not really their remit.
You could report it to the college but again it is not really a professional misconduct issue. It is just a mistake. One can argue a negligent one but that isn't a college issue unless actual harm to an animal is caused.