It is the "deemed" delivery date that counts, not the actual delivery date unless, as mentioned above, it can be proven. Most of these companies now use bulk mailing services and some of these will be able to produce a "proof of mailing" certificate.
However, as far as POPLA is concerned, they wouldn't care. In court though, it would be a different matter.
The operator would argue that the NtK was sent on a particular date and show a copy of the NtK. However, without either a proof of posting certificate or a signed for delivery receipt it would be your word against theirs.
If you have an independent witness who could confirm the actual delivery date, that would add much weight to your statement. Also, you would have even more weight if you highlight that the claimant has simply stated that the notices were sent but has provided no proof of service, shifting the burden of proof onto them. By referencing CPR 6.26, you emphasise that producing a copy of the notice is not enough to establish service and that they need to prove that the notices were posted and properly delivered.
You would argue that the claimant has provided no proof of postage or certificate of service, making it impossible for them to rely on the presumption of service under CPR 6.26. The claimant must show evidence such as proof of postage to assert that the notice was actually sent.
The claimant might argue that if all the other correspondence was received, then on the balance of probabilities, the NtK was also received. By pointing out that this is speculative and not based on evidence, you further weaken the claimant's position. This also invites the court to consider whether the notices were sent or properly delivered in the first place.
By summarising the failure to prove service, the court would need to consider whether the claimant has sufficiently demonstrated compliance with the relevant rules of service and whether they can pursue the claim based on defective or missing evidence. Add to that an independent witness statement, it would be difficult for the court not to accept your version.
We are a long way off anything like that, if ever. Just keep your powder dry for now and wait and see what POPLA decide.