There's a presumption in proceedings with a public body that it is acting properly and its statements can be believed. It's called the presumption of regularity. I consider that H&F aren't entitled to it. My word doesn't count but evidence of the Council's irregular actions (as I set out below) may persuade the adjudicator to puncture the presumption.
It's your call as to what you put in your appeal. Here's what I would say:
There seems some confusion as to what exactly the alleged contravention is. The contravention code, 52M, applies to a failure to comply with the terms of a TMO, in this case TMO 2037 dated 18th September 2024. The rejection of my representations refers to my passing the "flying motorcycle" sign as though that is the contravention. In normal circumstances the presumption of regularity would make the two propositions identical.
I consider that in this case the Council aren't entitled to the presumption of regularity for the following reasons:
1. Great West Road is a TfL road and TfL's ownership extends at least as far as the combined cycleway/footway to the north of the carriageway.
2. The Council's plan of the signage, https://www.whatdotheyknow.com/request/rivercourt_road_experimental_tmo/response/3055381/attach/3/Rivercourt%20Road%20A4%20Junction%20Layout%20Plan.pdf, confirms this and also shows that TfL's land on the west side of the exit slip road runs to where the "RED ROUTE // CLEARWAY // End" sign is.
3. Under section 121B of Road Traffic Regulation Act 1984, the Council is obliged to give notice to TfL before doing anything to one of the Council's highways which might affect TfL's road, let alone changing road markings on TfL's land. The Council also needs to comply with any instructions from TfL.
4. The Council has erased TfL's edge-of-carriageway markings on Great West Road and painted new white hatching with a solid boundary on either side of the exit slip road, across TfL's cycleway/footway. Those road markings now prohibit all vehicles, including pedal cycles, from crossing them.
5. The answer to a question to the Mayor of London about Rivercourt Road, https://www.london.gov.uk/who-we-are/what-london-assembly-does/questions-mayor/find-an-answer/a4-and-rivercourt-road-low-traffic-neighbourhood, refers to changes to be made to the signage "to remedy the situation". That indicates that TfL wasn't consulted before the Council made its changes.
6. The Council's answer https://www.whatdotheyknow.com/request/rivercourt_road_experimental_tmo/response/3055381/attach/4/Response%20all%20information%20to%20be%20supplied.pdf to FoI request 16918890 sets out the Council's view as to where the boundary lies between Great West Road and Rivercourt Road and where "a point 8.30 meters south of the southern building wall of No. 17 Rivercourt Road" lies. The boundary is the start of the one-way south-to-north restriction while the point defines its end. By my reckoning, the line across Rivercourt Road from the point, i.e. the end of the south-to-north restriction, lies south of the start, so the defined restriction doesn't exist and the TMO is unenforceable.
7. Paragraph 4 of the TMO stops half way through. If it means anything, it is that the entire section of Rivercourt Road between Great West Road and King Street is prohibited to all motor vehicles northbound. Other motor vehicles can enter it southbound from King Street but are prohibited from turning round and returning to King Street. Nor can they exit to Great West Road. They are trapped and will pile up until the road is blocked. This adds to the TMO's unenforceability.
Given this evidence, I consider that the Council needs to explain just what the TMO means, where it applies, how it relates to the signage which has been placed and demonstrate that there was a contravention.
P.S. This attack on the presumption of regularity is independent of the details of your case and may be of use to others wishing to challenge PCNs on Rivercourt Road