Free Traffic Legal Advice

The sign on the opposite side of the road is irrelevant to your case, because each side of a road is separate from the other side when restrictions are imposed. Of course restrictions can be identical, but often aren't, like here.  The reason the other side has a sign is because the restricted hours are different to those on the CPZ signs you see on entry to the zone. Councils are allowed to create CPZ, where the hours on the entry signs define the single-yellow line times, but also put up signs within the zone if they want to vary those times in certain locations. For me it is bad practice, but it is legal.

At the moment, based on your narrative, you seem bang-to-rights. Did you drive past the CPZ sign in your photograph, or come down the other way and turn left ?

I would not want to risk the CPZ argument when the sign is as close as it is. Better to argue inbuilt unfairness caused by two methods of signing being illogical. I have a top secret procedural impropriety strategy which is worth a go in this case.

Does the fact that there is a considerable distance between the one CPZ sign I passed and my parking space make an appeal more likely to succeed?

Well, it depends on what one defines as "considerable distance".  When the regs for CPZs came out there was guidance that essentially said these zones should not be larger than about 10 streets, (I forget the exact numbre) but nothing about distance. In practice, appeals based on this seldom succeed. The fact is you passed one of the signs. I'm afraid you need to be alert in London, and any time you park on a single yellow line without any signs defining the restriction, it is pretty certain that you are in a CPZ and need to be sure you're outside the restricted times.