You've been busy.
The council's photos show you bang to rights by clear DYL with double kerb blips which mean no waiting or loading. Your account doesn't suggest you have any viable statutory defence as regards the contravention. The only procedural blip as regards the PCN is that you were opposite and not outside 329 and this refers to Walworth Rd, not Cadiz St.
Their website is another matter: The amount outstanding on the Penalty Charge Notice will increase to £160.00 on Sun, 13 Jul 2025. Please pay £80.00 now.
Which is nonsense.
PCN issued 22 June;
Discount available until 5 July;
Earliest date on which the full penalty of £160 applies is 6 July;
Earliest date for serving a NTO(demanding £160 from keeper) is 20 July.
Whichever way you cut it, 13 July is wrong.
Other posters can assess whether taking this point forward is worthwhile.