So, in terms of why you can't be liable as the hirer... Private parking charges are based on contract law. The driver (allegedly) enters into a contract with the parking company whereby he agrees to abide with the conditions of the parking contract, as detailed on the relevant signage on the site, 'agreeing' to pay a parking charge of £100 if he does not. That contract exists between the driver and the parking company.
The parking company have no idea who the driver is, unless you tell them, which makes it rather hard for them to enforce against the driver.
There is a piece of legislation, Schedule 4 of the Protection of Freedoms Act 2012 ("PoFA"), which provides a mechanism for parking companies to hold the registered keeper, or the hirer of the vehicle, liable for a parking charge, in cases where they do not know who the driver is. However, there are a number of conditions set out in PoFA, and only if these conditions are met can a parking company hold the keeper/hirer liable. One of those conditions is that the place where the car was parked/stopped is "relevant land". PoFA defines relevant land as:
"(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.
The bit I have highlighted in bold is relevant here. Gatwick Airport is subject to byelaws, which govern all sorts of conduct within the airport land, including parking. This means the airport is not "relevant land" for the purposes of PoFA, meaning they cannot hold the keeper/hirer liable for any parking charges. They can only hold the driver liable, and unless you tell them, they don't know who the driver is!
It's a complicated sounding argument, but it's a well-trodden one, and the appeal suggested further up sets it out to NCP, who are well aware of it, and are likely to cancel.