Free Traffic Legal Advice

I definitely did this journey, I'm not sure exactly where this location is (but here is Google Maps link https://maps.app.goo.gl/xHaJKKcxU32VwPLr7) . I don't recall seeing this arrow. On the two photos (https://photos.app.goo.gl/gzJ1oH6dqz8yAgtz9), the first one is my correct registration plate YY08 GOC. In the second photo, the pale white car turning left is not my car. I cannot identify my car in the second photo (they have superimposed the registration number of my ca on the bottom right of the second photo)

Where's the PCN?

OP has posted it, but called it 'photos'

OP, you should call TfL and get them to send you their video of the alleged contravention. It comes as a DVD and also they freeze the process for 2 weeks. Once we can see it, a possible appeal argument may suggest itself.

Here is the approach to the junction on Parkway. You'll see the "straight-ahead only" arrow on the traffic signal head, and also the green phase showing a straight-ahead arrow. Picture on the PCN shows you making a left turn hence the PCN.
https://maps.app.goo.gl/aexmBupsEFtH2wwb9

I have just received the DVD, and I am definitely doing a left turn, which as your photo showed, is not permitted. The lower PCN charge is frozen until 22Apr25. Is there any possible defence I could use? I suspect I just have to pay up. Thanks in advance for any guidance. I am not familiar with this part of London, it was night time, and clearly I was not paying enough attention.

Frankly, I cannot see any argument against the PCN itself. Traffic lights have a "Straight Ahead" arrow on them, and also the green phase is a green arrow pointing ahead as well.

So you'd be looking at a "technical" appeal based on TfL mismanagement of the enforcement process. One of the regulars on here has developed these and you could well win your case on this alone despite the contravention being made out, so wait a bit, but don't miss the deadline on the PCN for paying or submitting representations.