"NHS/Rivers mix up - I'm left to pay the price"

After being referred by my GP to either the Rivers Hospital or Princess Alexandra for an X-ray of my broken collarbone, we decided to go to the Rivers to have this done as it is closer to where I live and more convenient. At no point were we told that this would not be an NHS appointment and the referral slip given for the procedure was from an NHS GP. Upon arrival at the Rivers Hospital, the receptionist at the clinic didn't ask whether I had private insurance at any point but instead, simply took the referral slip and asked me to take a seat. I then had my X-ray and was presented with a bill for £114. I queried this with the radiologist who took my X-ray and was told that she would ask the clinic manager to have a word with me. At this point, my mother and I were taken into an office and told we would have to pay this bill as it was 'our fault' for coming to a private hospital. We stressed again that we had been referred through the NHS and shouldn't have to pay but were made to feel like absolute criminals by the clinic manager who said we should have thought to ask at reception if the treatment was free or not. This is absolutely not the responsibility of the patient, especially one who has a valid referral. As we stated we did not feel we should pay for the X-ray, the clinic manager then said she had spoken to the hospitals finance department and as a gesture of good will the bill would be reduced by 50% to £57. Obviously we were still unhappy at having to pay any money at all for what should have been a free procedure, however in order to proceed in the correct manner and progress the situation we decided to pay this reduced price and begin a formal complaint. I am thoroughly dissatisfied with the way in which the Rivers Hospital handled my case and will not be using this hospital again in future.