I think front gardens where they're not contained by fence/hedge can be a grey area too.

'Gardens' are explicitly excluded as 'Off-Road', so the question may become When is a garden not a garden ? Similarly the OP says this area is a lined-off part of a car park, which is also excluded, so a further question may be What is the legal difference between 'public' and 'private' car parks ?

Markings such as those described by the OP may well mark the edge of the carriageway and delineate the area maintained at public expense.

Whether land beyond there is private may be a different question as at least for some purposes, including compulsory insurance, private land to which the public has access is treated as part of the highway. Classic example would be a supermarket car park.

I think front gardens where they're not contained by fence/hedge can be a grey area too.

Absolutely spot on as I understand it. When the law was changed I was involved on the committee of the local Motor Club and it for a time appeared to be putting the existence of Motorsport in the UK in doubt since if applied any car on the track would have needed tax/MOT/insurance despite the public being unable to access the actual track area. The lawmakers considered that the actual "facility" was all accessible by the public. Luckily common sense prevailed in that case.

But the point regarding front garden with no hedge/fence etc is a very good one.