Looking at the website, it appears more like some individual entrepeneur's money-making idea (and that's putting it kindly) than anything to do with the authorities. None of the 'sites' are in what we'd call remote locations, and there are so few of them that it's obvious this is a new 'startup' of some kind - a kind of AirBnB for farmers/landowners. You have to dig deep into the site to find any indication of who might be behind this, and the only reference I can find is to a (possible) company called The Bridge Strategy, of which I can find no trace at Companies House under that exact name. The closest match is The Bridge Strategy Implementation Ltd, a Harrow-based enterprise of seemingly little importance, which may or may not have anything to do with the operation.
Turning to the Guardian article. Whether the 'Will Harris' of "Rewilding the Humans" (at least one person has reviewed it on Amazon) published by "The Waterloo Bridge" (of whom I can find no trace) is a part of this enterprise is unclear. I would love to know, however, the basis for Phoebe Smith (Guardian Reporter)'s headline claim that this is a "pilot scheme launched to promote wild camping in two of England's national parks". It strikes me as nothing of the sort. So, rubbish journalism and a micky-mouse business operation.
I've written to ukwildcamp.org asking for details of the individual(s) and/or promoters behind their enterprise, and whether it has any connection with any statutory authority. I'm not holding my breath.
In common, I imagine, with many others here, I'll prefer to carry on 'taking my chances' for the moment. It'll be a good while before much by way of enforcement action occurs. In any case, as I see it you're still not committing an offence by wild camping in the Lake District without permission (paid or otherwise); it's a civil matter for which you can theoretically be sued for damages and/or required to move on. New legislation would be required before any statutory penalty could be applied. In effect, all this £20 'booking fee' gives you is permission to camp at a specified spot, and thus exemption from civil action.
On reflection, I suppose it's inevitable that with the growing numbers of people taking to the hills etc, there's going to be various attempts at extracting money from them.
On a positive note, this could affect sales of the more brightly coloured tents.