You cannot can only do one of two things on receipt of a Charge Certificate (CC), pay it, or ignore it and wait for the next statutory document to be sent to you, the Order for Recovery (OfR). At the OfR stage, you can submit either a Witness Statement, or a Statutory Declaration. Which one depends on what legislation the PCN was served under. For London, parking PCNs will be under the Traffic Management Act 2004, so require a Witness Statement, and moving traffic offences will be under London-specific Acts like the London Local Authorities and Transport for London Act 2003, which require a Statutory Declaration.
Once the CC payment period expires the council can register the debt at the Traffic Enforcement Centre. This adds £10 to the CC amount. From this point you need to be proactive and check for registration of the debt every week. You can do this by checking the amount owing on the Lewisham webpages. Once the amount goes up by £10, the debt is registered and the OfR should be on its way, and this will include the SD form. However, as you have missed getting the letter rejecting your reps, it is probably a better idea to download the form from the TEC website, and submit it without having seen the OfR document. The form to use is the PE3. Do NOT fill it in without coming on here to make sure you have filled it in correctly. The slightest error will result in it being rejected. Provided you submit it within the time allowed, it will be automatically accepted, and the OfR and CC cancelled.
Having now looked at the PCN and video, the PCN is for passing a 'Flying Motorbike" sign on Dacre Park at the Lee High Road end. The video does indeed show you turning into Dacre Park, but you are not shown as passing a restriction sign as above. A look at GSV of June 2024 also shows that the actual signs that bar motor vehicles are not at the entrance to Dacre Park but some yards in. So in my view, the video shows no contravention whatsoever. The signs are located just under 27 metres from Lee High Road. Of course the signs may have been moved closer to Lee High Road since June 2024, only you can tell us if this is the case, but in my view they have not proved the contravention.
So when you do manage to get the matter reverted back to the PCN stage, you could argue at London Tribunals that the video evidence shows no contravention.