With most minor legal issues, there are 2 parts - what does the applicable law say, and when happens in practice.
For example, if in practice the prosecution invariably drop the case if you blink first, the law is of little consequence.
As has been said, there is currently nothing to appeal - you can accept their offer of an out of court disposal, or you can decline/ignore it and they can subsequently prosecute you or not.
As far as I can tell, their comment about s. 87 EPA 1990 is a big fat lie (specific legal term) - actual legislation
here. However, whether or not their pants are on fire has little bearing on whether or not they can prove beyond any reasonable doubt that you committed the actual offence created by s. 87 (as opposed to the one they made up to try to intimidate you).
In a criminal trial, the court have to be certain beyond any reasonable doubt that the accused committed the offence. This is not quite the same as the flawed belief that the prosecution must prove their case beyond any reasonable doubt. The way that a trial works (in theory) is that the prosecution present their case (evidence and legal argument) and then the court decide whether or not there is a case to answer (whether they are satisfied on the balance of probabilities that the accused is guilty). The defence then present their case, and the court can take such inferences as might be proper from the accused's refusal to give evidence, although they cannot convict on inference alone. If at the end of the defence's case they are satisfied beyond any reasonable doubt that the accused is guilty, they will convict.
For future reference (doesn't help you now), if you're going to seek legal advice, do so before doing something that could potentially paint you into a corner.
"No comment" in an interview under caution can give rise to the inference that if it wasn't you, you would have said so".
However, if you had declined to answer until such time as you had obtained legal advice, that cannot be held against you.
In relation to a note inviting you to incriminate yourself, I would not consider that to be an interview until such time as I responded, which would be sometime around "never" - unless I had some defence that I wanted to set out at the earliest opportunity. I do not believe that ignoring the letter could have been held against you.
I would suggest that if material addressed to you was found in illegally deposited litter, that raises a case to answer that it was you who deposited it. On its own it is not proof beyond any reasonable doubt, but combined with inferences that a court might make of your "no comment" "interview", it could be. The obvious questions is, if you didn't deposit the litter, what reasons might you have had for declining to comment (other than bloody-mindedness).