(Sorry, me again) There is only one sure way that you can, at the very least, increase some efficiency in the NHS and that requires the full-time services of a regiment of trained snipers using high velocity, hollow-tipped rounds with 100% head-shots guaranteed. At least that way you can get rid of the old and demented, the druggies and highly dependant alcoholics etc.
One size does not fit all in a public health service. Imagine you ran a car plant producing a range of five family saloon cars. Then one day you get a letter from the department of transport insisting that you also produce; buses, tractors, tanks, fire engines, diggers and HGVs all from the same single manufacturing plant that you use for your saloon cars. Oh, and you won't be told in advance how many of each type are needed each week either. That's what the NHS is like - there is no way on earth that you can tell what size, shape and age the problems are going to be and yet they continue to walk in through the door 24/7!
You can't just say oh look demand on the renal unit is down 40% in the last month, well then, we can shift half of the ward and equipment over to maternity, they seem to be constantly dealing with babies over there! There is very little if any predictability to work with.
The NHS is a bit like a prism - the white light of constant patient demand that streams in through the front door is then separated out into a broad spectrum of complaints and dealt with accordingly. So what looks like a single line of uniform customers actually represents a whole gamut of things that need fixing.
Of course if you want to increase efficiency further down the line, in the output stage, you could provide well funded, well staffed and well trained NHS community outreach services for say drug and alcohol dependency units. Success in that area would almost certainly release some resources in other public facing areas, such as policing, probation and the courts etc. Those released resources could then be re-directed to more urgent policing matters etc.
So it is an almost impossible task to achieve efficiency in general. That's not to say that you can't spend resources carefully, with hindsight and juggle rotas/be flexible with agency staffing etc., but in the main the demands still require constant flexibility and there is always a cost to that. Then again, you can push that flexibilty too far and, guess what, it breaks!