You have the absolute right in law to now take them to London Tribunals, but you'd need to strengthen the advance signage issue, (obscured by tree foliage). You'd then need to convince them on not seeing the restriction signs until too late.
I did some measuring on the distance across the junction from the traffic lights stop line to the entrance to the restricted route, and it is 30.5 metres, (or just over 33 yards). In my view this is quite a long distance, so if you missed the advance sign, you'd be in danger if you saw the signs half-way across the junction, not forgetting that they have a text board on them with times and allowed vehicles which would be impossible to read until your just about on it. Clearly the council recognised this and erected the advance warning sign.
Of course, if you take them to London Tribunals, it is with the full PCN penalty in play, but no more than that. I suggest that if you take this course, you get some photos taken from a driver perspective, of the the advance sign.
very little chance of actually appealing the fine
Well, here are the words of the Earl of Montrose. Which are you, fear of your fate, or the benefit of winning is not big enough ?
"He either fears his fate too much
Or his deserts are small
Who fears to put it to the touch
To win, or lose it all!"