You can rebut this but it’s not likely to be simple to do so.
This is true, but I'd argue that it's true for a slightly different reason than the one you propose.
NCP will state that they’re not responsible for postal delays and that they posted it in time.
PoFA requires them to ensure the notice is 'given' within 14 days. If they choose to do that by sending the note by post, and it subsequently arrives late, that's their problem. If the OP can prove (on the balance of probabilities) that the notice arrived outside of the required timeframe, then he will have proved that NCP failed to comply with PoFA. The fact the delay is Royal Mail's fault is immaterial. The issue for the OP is that PoFA also includes a provision that notices sent by post are presumed to be delivered on the 2nd working day after posting, unless the contrary is proved. Proving the contrary is of course very difficult.
Do you have any other photos of the signage? The ones you've shown us set out the means and deadlines for payment, but don't appear to contain the key contractual terms NCP will need to rely on to enforce the charge.