There are two aspects to this.
First of all, you were convicted by a court under proceedings of which you were not aware. The normal way to deal with this is to make a “Statutory Declaration” to that effect. The conviction and all the penalties that went with it are expunged and the charge(s) will be put to you again.
In your circumstances, provided you were the driver at the time of the speeding allegation, you can ask the prosecutor to drop the “Fail to Provide Details” (FtP) charge if you plead guilty to speeding. This is usually accepted and - provided your speed was not particularly excessive - you will finish up with a much less serious conviction (with a lower impact on any future insurance premiums), fewer points and a lower fine.
The other issue is the level of the fine. Firs of all, the speeding charge is a dead duck as they have no proof that you were driving. The FtP offence attracts a fine of 1.5 times your net weekly income. Since the court had no details of your income, they would have used a default figure of £440pw. As well as that you will be charged a “victim surcharge” of 40% and prosecution costs. So you would have been fined £660, a surcharge of £264 and £90 costs which equals £1,014.
If you want to go through that process it is unlikely that you will be able to do so without attending court. But it’s worth a try.
If you simply want to challenge the level of the fine, the normal way to do that is to ask to to have your case reopened under s142 of the Magistrates’ Court Act. That section is designed principally to allow mistakes to to be rectified. But if the court had no details of your income, they would have proceeded perfectly properly in imposing a £660 fine, so I doubt a request to reopen would be successful. In any case, it would only be beneficial to you if your weekly income is less than £440. If it is more, you could find the fine increased.
I cannot progress through the process you have provided a link to because I do not have a valid URN, so I don’t know how it works. But I would imagine, depending on your responses, it will guide you to one or other of the two processes I described.
If you’re not bothered about the conviction, the points and a “totting up” disqualification (as well as the impact all that will have on any future insurance premiums) then there’s really no point in doing much at all.