I work in the NHS. We have been finding "efficiency savings" every single year I've been working in the NHS. This means different things depending on the timing.
Some of it is genuine efficiencies like where you have 2 "competing" services that are employing full time staff a few miles apart and neither place has enough patients to run full time so it makes sense to combine them. This is rare though. The majority of the time it means someone has left and we'll see if we can get by without replacing them so everyone else's workload, that was already at capacity, gets increased. In the NHS that typically reduces safety and quality or just increases the waiting list. Another efficiency saving is when someone retires, recruit their replacement at a lower band so they are getting underpaid and end up off work with stress. It means getting rid of anyone that isn't clinical so the clinical staff spend half their time doing admin/management/meetings instead of seeing patients.
Anyone looking at that would instantly spot that all of those measures do the opposite of increasing efficiency. They might reduce the bottom line but that isn't the same as being efficient. They are cost-cutting measures that typically end up costing more in the long term. If you give a consultant 5/10 sessions to see patients they will realise they are better off being paid to just see patients privately and not have to get involved with all the admin/teaching/management side of stuff. That means you end up with staff shortages and paying premium agency prices to see the patients they would have been seeing anyway.
I wish more people were aware of how hospitals were funded. They are told this is your target activity and this is how much income you will get. If they can't/don't do it they get less income. There is an often trotted out line of "too many managers" but the opposite is true. There aren't enough. All the managers are essentially just rota planning. They don't have the time to actually manage or improve performance. It's just constant negotiating with a small pool o clinicians/nurses/AHPs to get them to cover shifts. Those people are then expected to calculate what their "activity performance" will be but if the numbers are genuine they are told they are too low so they are given unreachable targets or risk losing funding. They can't control most things that affect performance. If a theatre has capacity for 8 people a day they can plan to do 8 but if the ward can only hold 6 there is wasted theatre time. If the imaging department can't do all the scans they can't do anything about it. If there are new patients coming in via A&E they can't prevent it. If the patients need social care but there's nowhere to send them they sit in a bed for weeks and that's capacity that can't be used for new patients.
It's incredible how inefficient the constant efficiency savings make an organisation.