With ref. to making-up usurious charges "on the spot"....my understanding is that, in catering, if there is a dispute, one can, indeed, proffer what one considers a resonable payment, together with one's name and address. - It's then up to the caterer to pursue the matter in a Civil court.
Where a landing (unauthorised) is concerned, I would think that the landowner has a lien on the visiting machine. In practise, this means that the landowner would take temporary "ownership" of it, with attendant responsibility for care and safekeeping. again, a disagreement would need to be settled in Civil court.
The above scenarios apply when you leave your car in a repair-garage. Read the small print and there's usually a hefty "storage-fee" if you don't collect and pay promptly.(after all, you're depriving the owner of use of the area taken by your property. )
The getout is to pay by cheque , clearly marked " disputed charge paid under duress" - that gets your property back and leaves the door open to sue for return of unreasonable charges.
Not even a barrack-room lawyer, so this info may well be worth what you paid for it!