OP, the plain fact is that the council, ever greedy for your money will refuse whatever representations you present on the state of the double-yellow lines. They refuse all reps because they know that in doing so, most people, (like >95%) just cough-up. However, you have the absolute right in law, assuming you are the owner of the vehicle, if they refuse your reps, to take them to the adjudicators at London Tribunals for an unbiased decision on the adequacy of those DYLs you parked by. If you do, the full PCN penalty is payable if you lose.
The problem you have is that whilst the lines are in poor condition, it has been established at adjudications many years ago that provided yellow lines convey the restriction to a motorist, then they are adequate; perfection is not required.