A typical money-grubbing PCN that we see so often.
You clearly stopped having seen the sign, but the video doesn't show you reversing back out, (naturally !!). In addition, the restriction, (a single No Entry sign), is, in my view inadequate, and should have been placed on the nearside to emphasis its applicability. Two, one each side of the approach, would have been better. Councils are under a duty in LATOR Regulation 18 to place adequate signage to indicate a restriction. Typical English regulation, because who decides whether it is adequate or not ? The council who put up the signs, of course !!
https://www.legislation.gov.uk/uksi/1996/2489/regulation/18So your reps should contain two aspects, with recognition of the restriction but too late to avoid passing the sign, and the inadequacy of a single sign that lead you into the restriction. Do be aware that the council, ever greedy for your money, will refuse your representations, so you must be prepared to stand your ground and take them to London Tribunals. Driving a few yards past the sign then backing out is what I would consider a
de minimis contravention, and occured due to the inadequate signage.
You have the absolute right in law to take them to London Tribunals, but must accept that the full PCN penalty will be in play. I think the odds are reasonable, but it's not a slam-dunk win, I'm afraid.