If this is land owned/managed by Forestry England, it would seem to be land subject to the Forestry Commission Byelaws (https://www.forestryengland.uk/sites/default/files/documents/Forestry%20Commission_Byelaws.pdf). Some of those byelaws control parking on Forestry Commission land - this would mean it is not "relevant land" as defined by paragraph 3 of Schedule 4 of the Protection of Freedoms Act 2012 (PoFA) (https://www.legislation.gov.uk/ukpga/2012/9/schedule/4):
3(1)In this Schedule “relevant land” means any land (including land above or below ground level) other than—
(a)a highway maintainable at the public expense (within the meaning of section 329(1) of the Highways Act 1980);
(b)a parking place which is provided or controlled by a traffic authority;
(c)any land (not falling within paragraph (a) or (b)) on which the parking of a vehicle is subject to statutory control.
As a result of this, they cannot rely on PoFA to recover the charges from you as the registered keeper of the vehicle, despite the letter's claims to the contrary (we can deal with that later). As a result, assuming you are the keeper, you can appeal along the lines of the below, as the keeper only:
Dear Sirs,
I have received your Parking Charge Notice (Ref: ______) for vehicle registration mark _______, in which you allege that the driver has incurred a parking charge. I am appealing as the registered keeper of the vehicle. There is no obligation for me to name the driver and I will not be doing so. The car park at Leigh Woods forms part of land under the management and control of Forestry England. As such, parking on the site is subject to the Forestry Commission Byelaws 1982, meaning it is not "relevant land" for the purposes of Schedule 4 of the Protection of Freedoms Act. Accordingly, you are unable to recover the charges from me as the registered keeper.
I am therefore unable to help you further with this matter, and look forward to your confirmation that the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
If appealing online, be careful there are no drop down/tick boxes that cause you to identify who was driving, and keep a close eye on your spam folder for their response. If they do not respond within 28 days, chase them.