The dates show that, issued on 10 February, the notice is too late to transfer liability from the unknown driver to the registered keeper, with presumed delivery on 12 February being more than 14 days after the alleged transgression on 28 January.
So indeed they can not use PoFA to transfer liability and say that they’re not doing.
Their statement that they can assume you were the driver is complete twaddle. They make untrue statements like this in the hope that you will believe them and pay up.
You “appeal” by telling them that you’re not liable and not going to pay, essentially. It’s a common form of words which, if I find it, I will post here.