So what do you think might be a legally robust argument ? Presumably you did park on a single-yellow line during its restricted hours. You were there for 10-15 minutes. There are two exemptions to yellow lines, (1) loading/unloading, and (2) boarding/alighting passengers. Do either of these apply ?
In addition to the above, there may be a 'technical' appeal based on Haringey mismanagement of the enforcement process. Such appeals have nothing to do with the alleged contravention and are invariably dealt with at London Tribunals, with the full PCN penalty in play. Quite a few have now been won, but clearly, you are taking a double-or-quits gamble. If you win, you pay nothing, if you lost you pay the penalty, but there are no additional costs.