Although I have been told elsewhere this morning that admitting the offence, giving my driving licence details and paying my form online was not enough.
Apparently I should also have signed the paper copy of the form and posted it, which makes no sense at all as the online part was obviously to streamline and modernise the whole procedure.
That's incorrect. You only need to sign a form when providing the driver's details. You get the request for those details when you are sent the "Notice of Intended Prosecution". You must have provided them in order to be offered a fixed penalty and if you didn't (or failed to sign the form) you would have been prosecuted for failing to do so. That offence carries six points, not four, so you have been convicted of speeding.
I've just noticed in your original post that you said you "received 3 points" after you had sent off your £100. Are you sure about that? How do you know? You also said you have paid the £550.
I'm guessing but this is my take on what probably has happened:
You were sent a NIP and a request for driver's details.
You responded by naming yourself as the driver.
You were offered a fixed penalty.
You paid £100 and provided your licence details.
The police failed to process your licence details (for whatever reason).
You were prosecuted for speeding and were sent a "Single Justice Procedure Notice" (SJPN).
You responded by pleading guilty to speeding.
You were sentenced in accordance with the normal sentencing guidelines.
You paid the fine/costs etc. and have four points on your licence.
If I'm right, the only option for you is to ask the court which convicted you to reopen your case and ask them to re-sentence you at the fixed penalty level. Whether or not they will agree to your request depends very much on what you received and how you responded
Check what paperwork you were sent and how you responded.
