Like Manxman, I find this very mysterious.
First of all, let’s work on the assumption that only one allegation of speeding is involved.
If that was on 5th December, let’s say that a Notice of Intended Prosecution (NIP) and an accompanying request to name the driver (a “S172 notice) was sent within a week, say by 12th.
This would have been deemed served on you on Friday 14th.
You would have until January 11th to respond.
If you didn’t it is about right that court action would be initiated some time in March
(most areas send a reminder and they usually give the Registered Keeper another couple of weeks to respond).
So it seems quite likely that the conviction you have seen on your licence stems from that allegation and that it was heard in court in April.
As far as the police are concerned that matter is done and dusted.
You failed to respond to their request,
they prosecuted you for that failure and you were convicted and sentenced.
I imagine you owe the court £881.
That would be a fine of £660 (1.5 weeks’ net income based on a default figure of £440pw), £66 “Victim Surcharge” and £85 prosecution costs.
I’m surprised no attempt has been made to recover that sum from you.
But now it gets puzzling.
It seems that somebody has prompted the police to write to you.
I’ve no idea why that should be and I think you would be well advised to find out why they have sent the 7th October letter to you.
But it gets worse.
It now seems, from what you say, that they are prosecuting you again for an offence for which you have already been convicted and sentenced!
Is that correct, or are the SJ papers you have been sent simply a copy of those which you did not receive for the April hearing?
If indeed they do intend prosecuting you again you should tread carefully.
As Manxman suggests, you may have been able to do a “deal” to get the S172 charge dropped in return for pleading guilty to speeding. But you cannot do that as you are sure you were not the driver.
I think you need to find out:
(1) Why did they send you the 7th October letter? What makes them believe you were not in receipt of the earlier paperwork?
(2) Why are they apparently prosecuting you again for an offence for which you have already been convicted and sentenced (if indeed that is what they are doing)?
There is quite a bit of correspondence which takes place between being detected allegedly speeding and a court case.
It seems very odd that you received none of this but you did get the 7th October letter.
If you do engage a solicitor it will cost you a tidy sum and you are unlikely to be awarded all of your costs (you may not be awarded any at all, depending on the outcome).
I would make those enquiries as a matter of urgency before anything else.