So I’m looking for advice on how to appeal.
You don't, as you then correctly say you submit a statutory declaration which is NOT an appeal.
Pedantic much?
Technically, the OP could appeal to the Crown Court, but a stat dec is a far better solution.
Currently, the OP has been convicted of an offence in his absence and received a totting ban. He is seeking to challenge this conviction. If he was asking whether to do a stat dec, appeal to the crown court or appeal by way of case stated, stat dec, not appeal would be an appropriate response, but in the context of his post, the distinction is pedantry.
So I would plead not guilty to the charge of failure to notify on the basis I did not receive the notice sent.
What matters is not whether you didn't receive it but whether it was served or not, as a number of items of post (as least 3, more likely 4) were not received by you it suggests the Police did not have the correct address for you (despite what you say, as 4 items going missing is 'unlikely' I would suggest), perhaps you moved and forgot to update the V5c registration document address with the DVLA?
Spouting bollox after being pointlessly pedantic is not a good look!
There are 2 potential "defences" (for practical purposes) to the s. 172 charge - whether the notice was served, and whether it was reasonably practicable to provide the information. Not receiving the notice is not
in itself a complete defence, but if the circumstances were such that it would not have been reasonably practicable for the OP to ensure that such notices were brought to his attention and he was not aware of it, then it was not reasonably practicable to provide the information.
The speeding charge I was driving my son to hospital - can I plead not guilty? Or do I plead guilty and ask for mitigating circumstances?
Of course you can (and should currently) plead not guilty, whether you then continue that is a different matter, if the S172 notice was properly served (and you have to prove it wasn't) you will currently be found guilty of the more onerous S172 offence, as such offering to plead guilty to the speeding (when you can't then offer a defence) in exchange for the S172 being dropped seems the pragmatic option.
I agree that based on what the OP has told us, he should plead not guilty to both charges. It is uncertain from his account whether he has sufficient information to enable him to plead guilty (in theory you cannot plead guilty to an offence without knowing what the charge is and what material facts are being alleged - because that is what you are pleading guilty to) - although that is largely academic.
Some areas send guidance with the SJPN stating that if the accused pleads guilty to one of the offences, the other will automatically be dropped. If the OP has been provided with such guidance, then it might be advantageous to "do the deal" at the earliest opportunity, or not - depending on the strength of his defences if the charges went to trial.
The fact that the OP was taking his son to hospital is not
in itself a [complete] defence. It depends on the circumstances. I am not going to hypothesise about what possible circumstances might constitute a defence - we apply the law to the facts, not the other way round.
There is also the question of whether the OP could be asked whether he was driving when defending the s. 172 charge, or whether inferences could be made. However, if the OP's defence to the s. 172 relies largely on his credibility, running a technical defence to the speeding charge may not be helpful.
Driving your son to hospital is, of itself' meaningless unless you are suggesting it was some form of an emergency, obviously to a routine appointment is no different top driving to a book shop.
That.
There was a driving ban issued on the same day the points were added to my license but it’s not mentioned in the paperwork supplied in the email but is shown on my license online - driving ban due to totting up of points
Very unfortunate, this is where applying online is going to probably be bad, if you contact the court in person and speak to someone you may get your hearing expedited, whatever you put in an online application will probably not be looked at until it reaches the front of the queue - in some time from now.
Also, that.
The ban has been imposed by a court of law. Unless and until a court of law quashes or suspends the ban, you are banned - regardless of what defence you may be able to present. The stat dec would set aside the conviction and sentence, but you are banned until then - unless you can get a court to suspend it before then.