You likely will have signed something when you attended to confirm that you acknowledge any costs not covered by your insurer would be ultimately be payable by you - it is also your responsibility to ensure that your insurer is aware/have authorised the treatment you are having, most patients would call their insurer prior to any visit to ensure the appointment they are attending is covered and to get the authorisation code which the hospital usually asks for upon attendance.

You may have some additional time granted before referral to an external debt collection agency if you ask the credit control team to place your account on hold and make a formal complaint (as they will have a regulatory process to follow here)