Free Traffic Legal Advice

My local hospital's car park is managed by a company called LPS (Local Parking Security). It works on ANPR and you are supposed to pay before leaving.
I forgot to pay so I left without paying (and the barrier is always open). I realised my mistake after a couple of minutes and went back in, tried typing my number plate, but the machine was showing "no charge required", as it was probably referring to my second parking session. There was no number to call on the machine so I had to find the hospital's security office where they told me I had to call the company responsible for the car park (LPS) to pay over the phone and suggested to keep holding on the line even if nobody answered.
I'm home now and I've been on hold with LPS for 1.5 hours at the time of this post; it's already more than the time my car has been parked in that car park, nobody is answering, what can I do?

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I managed to call them 3 days ago; maybe I was just calling outside of office hours the first time, but this time they picked up in under 15 minutes and they took the payment over the phone (around £3) and the lady on the phone was really nice. The payment is showing on my bank account.

I realised my mistake after a couple of minutes and went back in, tried typing my number plate, but the machine was showing "no charge required", as it was probably referring to my second parking session.

So, it appears you've entered and exited by vehicle twice on the same day without paying. We've no idea what transpired in your telecon.

Let's hope the second time falls under a minimum time limit, so no charge due, and the payment made covers the first event in its entirety.

I'm certain you'll come back if necessary.