"If paying privately get a quote in writing"

Have recently been struggling with severe back pain and not getting very far waiting for NHS treatment. Rang Thornbury to enquire about private MRI quote between £400-£500. Went a head and booked as pain unmanageable by this point. Results came quickly and have now been referred for surgery within the NHS. However the invoice has arrived it's now £750 a substantial difference which they can't reason for other than to say the amount is variable depending on the area scanned. Had I been quoted this I would have looked further afield for more reasonable options. Very disappointed.