The part of a private medical bill your policy does not pay, leaving you to settle it.
A shortfall happens when the fee charged is higher than the amount your insurer will pay, when a limit has been reached, or when part of the treatment is not covered. Insurers publish fee schedules for recognised consultants, and using a consultant who charges within them is the usual way to avoid one. Asking the hospital and the consultant for the full cost in writing before treatment is the simplest protection.