But just being "electronic" doesn't mean efficiency. I've worked on computerising manual systems for decades (fair enough not NHS) mostly in accounting, stock control, costing, etc in small/medium organisations.
I've seen (and solved) some absolute howlers of "computerisation" where tens/hundreds of thousands of pounds was spent on "bespoke" specially written programs "because the organisation was complicated and couldn't possibly use off the shelf software". What the computer bods did was computerise a chaotic mess because the organisation were adament they were "so special" and unique! So, the end result was inefficient computerisation, sometimes it worked, most often it didn't and led to even more admin staff. Time and time again, we'd just scrap it and make them change their internal workings so that an off the shelf package would work!
The "best" was an oil rig electrical component firm. They had a convoluted stock numbering system that was a chaotic mix of numbers, letters, symbols and degrees - each product code was (from memory) 19 characters long. But then their design/drawing office also had their own numbering system which was completely different but similar - i.e. a mix of letters, numbers, symbols, degrees, etc but in a different order. It was so chaotic that they had their own internal department called "planning" where a dozen or so office bods made sense of it all by matching part numbers to drawings manually. The firm was growing rapidly and the whole admin was getting out of control. They had a "beauty parade" of IT firms who came in to review the processes and offer their solution. Quotes of millions were received for a company wide bespoke software solution. I was employed by their auditors, and we were asked for our opinions on their proposals and whether we had alternative solutions. Our team came up with our "solution" - it was an off the shelf system (Pegasus) that we knew well as we worked with it at other manufacturing clients - cost was £30k, we had only one criteria to make it work which was that drawing and parts numbers had to be changed into a coherent code - cue horrified stares from the board of directors, but when we explained how it worked elsewhere, they started to look interested. A year later, the implementation was complete, and it worked. The "planning" dept was redeployed temporarily to change the coding/numbering system which was a big task and took several months, and to keep control of it during the changeover period. After the successful implementation, the "planning" team were re-assigned over other departments to help liaison between departments. It was a whopping success at a fraction of the cost of the "bespoke" solutions which may not even have worked.