If the laws in the UK are similar to Ireland, and probably they are, then private companies have no official right to fine you.
I got clamped in a private carpark a couple months back. 120€ "release fee". No thanks, I'll remove it myself. I dropped the clamp (undamaged) into the local police station lost & found and haven't heard anything about it since.
In most cases, these private companies won't go as far court because the risk that they lose a case which could set a precedent against their corrupt practices.
If it's a council fine then it's a different story.
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