I do not know how people can entertain this myth that linux support is as expensive as windows. The stability of linux applications is incredible compared with the brutal changes of windows (xp -> vista/7 -> 8 -> 10). Remote administration is far more easier and deployment on many machines is trivial. Machines rot is a lot slower, reducing the cost of machine replacement.
IMHO, the main cost is replacing the old window support guys by linux support guys because people a rarely competent in both and erasing the windows way of thinking is very difficult. The new team has to learn the specific needs and manner of NHS. Once they have the same experience as the previous team, the cost should melt.
It's nothing to do with the support guys. It's do with the support by the vender.
When you deploy an os over something as large as the NHS, your going to hit a few snags, perhaps at the code level. You will need somebody who you can phone up, who will then go bug fix those issues.
Vendors like redhat have support licences that support this. And those licences are still fairly expensive.
If NHS was going to deploy a Linux Distribution, they will have to bring a Linux distribution vender onboard which would take the role Microsoft does now.
IMHO, the main cost is replacing the old window support guys by linux support guys because people a rarely competent in both and erasing the windows way of thinking is very difficult. The new team has to learn the specific needs and manner of NHS. Once they have the same experience as the previous team, the cost should melt.