Driver did a three point turn in there to come back out...
OK, seems reasonable, but TfL are extremely unlikely to give way, (they want your money), so you'd have to take them to London Tribunals with the full PCN penalty in play. If you're up for it, you'll first need to submit representations to TfL, then, when rejected, register an appeal at London Tribunals.
You can only turn left into Tyers St off Kennington Lane, and there is an advance sign as you approach : -
https://maps.app.goo.gl/xiEeE9ZK1ENvJNJD9then the sign as you turn is quite prominent : -
https://maps.app.goo.gl/ypqneZZHRAReBYKM6Of course the advance sign would be easily missed if you were following a bus or high-sided vehicle, and once you turn you are pretty much committed.
So I would submit reps on the basis of only seeing the sign as you turned in, so you made a U-turn a few yards into Tyers Street and drove back out. Post up their response when you get it.