As has presumably already been said - some posters have had the s. 172 dropped by simply pleading guilty to the speeding and not guilty to the s. 172, whereas others have been convicted of the speeding and then been tried for the s. 172. We have only heard of one case where the s. 172 wasn't dropped when a deal was requested - which was because the accused got somewhat cocky and tried to tell the prosecutor that he had no case.
If the deal is refused, then the stock advice is not to plead guilty to the speeding as they have no evidence that you were the driver.
Defending the s. 172 would be difficult as you committed the offence when you failed to respond to the initial notice. When the police offered you a second chance, arguably the requirement was for the information to be delivered to the police, not merely sent. If they had received it and then decided to prosecute for both it would arguably be an abuse of process. Assuming that they did not receive it, to defend it successfully, you would need to get a bench that directed themselves that as a point of law, the requirement was satisfied by sending regardless of whether or not it was actually received, found as fact that you did indeed send it, despite ignoring/losing the original requirement, and that the reminder somehow negated the original failure to provide the information. You might want to start by telling them to look into your eyes, the eyes, the eyes, not around the eyes.
Broadly speaking, if the deal is refused by the prosecution, damage limitation is pleading guilty to the s. 172, and not getting an extra 3 points unnecessarily for the speeding by pleading guilty to the charge they can't prove.