The private hospital will take patients who are higher risk when they are paying directly. Part of the fee paid by the patient or their insurance company is to pay an anaesthetist to be available, to assess any non-surgical post-op complications or to manage post-op pain relief (such as inserting an epidural). We, as an NHS, can't afford to have an anaesthetist (who not only looks after patients in theatre but also looks after patients in ITU) sitting around just in case they are needed post-op
That’s not actually the case. Private hospitals cannot take patients whose needs they cannot safely meet. They have very clear limitations on what procedures can be carried our after the Paterson Inquiry. It’s not about money for individual cases; it’s about the equipment and full range and experiences of staff required for higher risk patients. A few private hospitals in large cities do have some small critical care facilities but not many. All consultants work under practicing privileges normally, in private sector. They have the limitations on their practice made explicit in the agreement and cannot offer surgery the hospital is not resourced for.
The NHS does have consultants in critical care and on call at all times. They are usually intensivists not anaesthetists for level 3 critical care, although anaesthetists are also employed. They very rarely just do operations; they cover maternity epidurals, acute pain management, have oversight of deteriorating patients, cover theatres as well as manage every ventilated patient.
Most areas have anaesthetic consortiums that provide anaesthetic cover for both NHS and private sector and work together to ensure safe cover.
The lobectomy could be one of a number of operations from brain surgery to lung surgery to liver surgery to thyroid surgery. It simply means one lobe of an organ has been removed.