We do not normally undertake transplants on 'sick' patients. The typical recipient will be someone with long term kidney failure having dialysis a couple of times a week and living a normal life.
So I presume some chap at work was told a kidney had come up for him or her, and rather than bring the kidney to him, could he pop up to Sheffield.
Logically we would get a blood transfusion vehicle to drive the kidney to the patient - it lasts in ice for many hours. Failing that we used to get a traffic police vehicle to drive the patient up. I don't recall the NHS ever being charged but it was a matter of a few hundred pounds. Nowadays there is a contracted fixed wing service which goes to collect kidneys ie takes them from donors as well.
So the use of a police or SAR helicopter by a cash strapped NHS and a resource strapped police and SAR service does seem to be something that deserves a smack on the wrist