On the face of it, that sign is unlikely to be capable of forming a clear parking contract in the circumstances you describe.
1. It reads as a prohibition, not an offer
The primary wording is “No stopping / parking or waiting … No exceptions.” That is “forbidding” language. In contract terms, it does not obviously offer any licence to stop/park on stated terms; it purports to ban stopping/parking altogether. Where signage is purely prohibitive, the better argument is that there is no contractual offer capable of acceptance by a driver who stops, so the operator’s remedy (if any) would lie in trespass, which a parking contractor usually cannot pursue in their own name unless they are the landholder.
2. Even if a court treats it as a “contractual charge”, it is tied to double yellow lines
Crucially, your sign does not say “no stopping anywhere on the access road.” It says no stopping/parking/waiting “on the double yellow lines along the access road.” If there were no double yellow lines where the vehicle was, then on the wording shown the driver has not breached the stated term. At minimum, it creates a serious ambiguity about what is and is not prohibited.
3. The term is not sufficiently certain or transparent if the “double yellow lines” do not exist at the location
A contract term has to be clear and certain. If the sign relies on road markings to define the restriction, but the markings are absent where the vehicle was, the operator will struggle to show the driver was given clear notice of any restriction that applied to that place. Any ambiguity is generally interpreted against the drafter.
4. Practical evidential point
If you have contemporaneous photos showing (a) the exact place the vehicle was, (b) the absence of double yellow lines there, and (c) what signage was actually visible from that position and on the route in, that is strong evidence. The operator would then be put to strict proof of the vehicle’s precise location and the existence/visibility of the double yellow lines referred to on the sign.