Your options are to defend the s. 172 charge (somehow) or plead guilty to it.
On the face of it, you have no defence to the s. 172 charge beyond hoping that the prosecution somehow completely balls it up beyond the ability of the legal advisor to rescue them.
The s. 172 requirement (NIP) was legally served when it was delivered to your last known address, which is deemed to have occurred 2 working days after posting, unless the contrary is proved. The offence is committed at the expiration of the period of 28 days beginning with the date of service, if the required information is not provided.
There is a statutory defence of it not being reasonably practicable to provide the information. Case law (Whiteside) provides that not receiving the notice is not in and of itself enough to engage the defence - it would have to not been reasonably practicable to ensure that you were aware of such notices. On the face of it, you simply forgot or didn't bother to update your address on the V5C until the speed camera reminded you.
Whilst there is no statutory provision for the police to extend the time to provide the information, they often send out reminders allowing you extra time, and it would be deemed not to be cricket to prosecute you for the original failure if you complied with the requirements of any such reminders. You didn't.
S. 172, as with most motoring offences, is a strict liability offence. Whether you intended to commit it or not is irrelevant to the commission of the offence, and generally would not even constitute mitigation.
TL;DR - absent some compelling reason (that you have thus far declined to share with us) for not updating the address on your V5C when you moved, and not putting any other measures in place, you have no viable defence. You can either plead guilty and receive a 1/3 discount on the fine (and surcharge) and face prosecution costs of ~£90, or spend a day in court trying to defend it, and (if you lose) receive a fine of 1.5 x weekly take-home pay, 40% surcharge and ~£650 prosecution costs.