I think it varies depending on whether it's NR or a TOC who run the carpark - or who employs a contractor to run it on their behalf. NR almost certainly own the land, which may mean it's subject to the Byelaws in addition to any Conditions of Use imposed by the TOC or their contractor. If you have an interest in any specific carpark, best to see what Conditions of Use are displayed and if the Railway Byelaws are mentioned.
Does this have anything to do with parking charge notices? As one avenue of defence against certain charges can be the fact that the Railway Byelaws apply on station car parks, and thus parking is under statutory control and hence the usual provisions for recovering private charges from registered keepers don't apply.
As previously explained, it will depend on who owns and runs the car park.
My local station is managed by Northern and leased from Network Rail, including a small part of the car park. Most of the car park is leased from SYPTE and it's free for rail users. (Only opened about 5 years ago and we need twice as much space already, but that's another story.)
The warning signs refer to "railway byelaws", so where exactly do those laws apply? See sign below.
If you want chapter and verse go to pepioo.com and look up the various threads on this
In a nutshell. MOST car parks near stations are covered by by laws (TfL give a complete list) Where by laws are in force only the DRIVER is liable and is taken to court
The alternative offered by the Private parking thieves is offering a 'contract' for parking there , In effect what they are saying is
Pay us X pounds and we will get the TOC off your back,Which i think, is a bit dodgy in law and will be the ONLY way they get paid, if it goes to court it is a 'fine' and they dont get the money, that is why they will try every trick in the book to get the RK to pay, threaten CCJ ( wrong, CCJ is only applied should you fail to pay after being convicted in court) debt collectors ( no power in law unlike baliffs)
They way to deal with these cases is
1) NEVER say who was driving, it is not sffiencient for the PPC to assume the registered keeper was the driver
2) you then play letter ping pong with the PPC until 6 months is up and the bylaw times out.
The PPC then has 6 years to bring a claim against the driver, and as they do not know who that is they are stuffed
Anyway more info on pepipoo.com
Airports are exactly the same they are covered by bylaws